26 Search Results for "Okrasa, Karolina"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.1
Triangle Detection in H-Free Graphs

Authors: Amir Abboud, Ron Safier, and Nathan Wallheimer

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We initiate the study of combinatorial algorithms for Triangle Detection in H-free graphs. The goal is to decide if a graph that forbids a fixed pattern H as a subgraph contains a triangle, using only "combinatorial" methods that notably exclude fast matrix multiplication. Our work aims to classify which patterns admit a subcubic speedup, working towards a dichotomy theorem. On the lower bound side, we show that if H is not 3-colorable or contains more than one triangle, the complexity of the problem remains unchanged, and no combinatorial speedup is likely possible. On the upper bound side, we develop an embedding approach that results in a strongly subcubic, combinatorial algorithm for a rich class of "embeddable" patterns. Specifically, for an embeddable pattern of size k, our algorithm runs in Õ(n^{3-1/(2^{k-3)}}) time, where Õ(⋅) hides poly-logarithmic factors. This algorithm also extends to listing all the triangles within the same time bound. We supplement this main result with two generalizations: - A generalization to patterns that are embeddable up to a single obstacle that arises from a triangle in the pattern. This completes our classification for small patterns, yielding a dichotomy theorem for all patterns of size up to eight. - An H-sensitive algorithm for embeddable patterns, which runs faster when the number of copies of H is significantly smaller than the maximum possible Ω(n^{k}). Finally, we focus on the special case of odd cycles. We present specialized Triangle Detection algorithms that are very efficient: - A combinatorial algorithm for C_{2k+1}-free graphs that runs in Õ(m+n^{1+2/k}) time for every k ≥ 2, where m is the number of edges in the graph. - A combinatorial C₅-sensitive algorithm that runs in Õ(n² + n^{4/3} t^{1/3}) time, where t is the number of 5-cycles in the graph.
Cite as

Amir Abboud, Ron Safier, and Nathan Wallheimer. Triangle Detection in H-Free Graphs. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 1:1-1:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{abboud_et_al:LIPIcs.ITCS.2026.1,
  author =	{Abboud, Amir and Safier, Ron and Wallheimer, Nathan},
  title =	{{Triangle Detection in H-Free Graphs}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{1:1--1:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.1},
  URN =		{urn:nbn:de:0030-drops-252885},
  doi =		{10.4230/LIPIcs.ITCS.2026.1},
  annote =	{Keywords: fine-grained complexity, triangle detection, H-free graphs}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.11
Classical and Quantum Polynomial Freiman-Ruzsa Algorithms

Authors: Srinivasan Arunachalam, Davi Castro-Silva, Arkopal Dutt, and Tom Gur

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We prove algorithmic versions of the polynomial Freiman-Ruzsa theorem of Gowers, Green, Manners, and Tao (Annals of Mathematics, 2025) in additive combinatorics. In particular, we give classical and quantum polynomial-time algorithms that, for A ⊆ 𝔽₂ⁿ with doubling constant K, learn an explicit description of a subspace V ⊆ 𝔽₂ⁿ of size |V| ≤ |A| such that A can be covered by K^C translates of V, for a universal constant C > 1.
Cite as

Srinivasan Arunachalam, Davi Castro-Silva, Arkopal Dutt, and Tom Gur. Classical and Quantum Polynomial Freiman-Ruzsa Algorithms. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 11:1-11:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{arunachalam_et_al:LIPIcs.ITCS.2026.11,
  author =	{Arunachalam, Srinivasan and Castro-Silva, Davi and Dutt, Arkopal and Gur, Tom},
  title =	{{Classical and Quantum Polynomial Freiman-Ruzsa Algorithms}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{11:1--11:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.11},
  URN =		{urn:nbn:de:0030-drops-252987},
  doi =		{10.4230/LIPIcs.ITCS.2026.11},
  annote =	{Keywords: Additive combinatorics, sublinear algorithms}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.5
Kernelization for H-Coloring

Authors: Yael Berkman and Ishay Haviv

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
For a fixed graph H, the H-Coloring problem asks whether a given graph admits an edge-preserving function from its vertex set to that of H. A seminal theorem of Hell and Nešetřil asserts that the H-Coloring problem is NP-hard whenever H is loopless and non-bipartite. A result of Jansen and Pieterse implies that for every graph H, the H-Coloring problem parameterized by the vertex cover number k admits a kernel with O(k^Δ(H)) vertices and bit-size bounded by O(k^Δ(H)⋅log k), where Δ(H) denotes the maximum degree in H. For the case where H is a complete graph on at least three vertices, this kernel size nearly matches conditional lower bounds established by Jansen and Kratsch and by Jansen and Pieterse. This paper presents new upper and lower bounds on the kernel size of H-Coloring problems parameterized by the vertex cover number. The upper bounds arise from two kernelization algorithms. The first is purely combinatorial, and its size is governed by a structural quantity of the graph H, called the non-adjacency witness number. As applications, we obtain kernels whose size is bounded by a fixed polynomial for natural classes of graphs H with unbounded maximum degree, such as planar graphs and, more broadly, graphs with bounded degeneracy. More strikingly, we show that for almost every graph H, the degree of the polynomial that bounds the size of our combinatorial kernel grows only logarithmically in Δ(H). Our second kernel leverages linear-algebraic tools and involves the notion of faithful independent representations of graphs. It strengthens the general bound from prior work and, among other applications, yields near-optimal kernels for problems concerning the dimension of orthogonal graph representations over finite fields. We complement our kernelization results with conditional lower bounds, thereby nearly settling the kernel complexity of the problem for various target graphs H.
Cite as

Yael Berkman and Ishay Haviv. Kernelization for H-Coloring. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 5:1-5:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{berkman_et_al:LIPIcs.IPEC.2025.5,
  author =	{Berkman, Yael and Haviv, Ishay},
  title =	{{Kernelization for H-Coloring}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{5:1--5:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.5},
  URN =		{urn:nbn:de:0030-drops-251376},
  doi =		{10.4230/LIPIcs.IPEC.2025.5},
  annote =	{Keywords: Kernelization, Graph coloring, Graph homomorphism}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.8
Binary k-Center with Missing Entries: Structure Leads to Tractability

Authors: Tobias Friedrich, Kirill Simonov, and Farehe Soheil

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
k-Center clustering is a fundamental classification problem, where the task is to categorize the given collection of entities into k clusters and come up with a representative for each cluster, so that the maximum distance between an entity and its representative is minimized. In this work, we focus on the setting where the entities are represented by binary vectors with missing entries, which model incomplete categorical data. This version of the problem has wide applications, from predictive analytics to bioinformatics. Our main finding is that the problem, which is notoriously hard from the classical complexity viewpoint, becomes tractable as soon as the known entries are sparse and exhibit a certain structure. Formally, we show fixed-parameter tractable algorithms for the parameters vertex cover, fracture number, and treewidth of the row-column graph, which encodes the positions of the known entries of the matrix. Additionally, we tie the complexity of the 1-cluster variant of the problem, which is famous under the name Closest String, to the complexity of solving integer linear programs with few constraints. This implies, in particular, that improving upon the running times of our algorithms would lead to more efficient algorithms for integer linear programming in general.
Cite as

Tobias Friedrich, Kirill Simonov, and Farehe Soheil. Binary k-Center with Missing Entries: Structure Leads to Tractability. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{friedrich_et_al:LIPIcs.IPEC.2025.8,
  author =	{Friedrich, Tobias and Simonov, Kirill and Soheil, Farehe},
  title =	{{Binary k-Center with Missing Entries: Structure Leads to Tractability}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{8:1--8:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.8},
  URN =		{urn:nbn:de:0030-drops-251403},
  doi =		{10.4230/LIPIcs.IPEC.2025.8},
  annote =	{Keywords: Clustering, Missing Entries, k-Center, Parameterized Algorithms}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.18
Bridging Treewidth and Clique-Width via Cograph-Modular-Treewidth

Authors: Václav Blažej, Satyabrata Jana, M. S. Ramanujan, and Peter Strulo

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
Many classical graph problems - such as Max Cut, Chromatic Number, Edge Dominating Set, and Hamiltonian Cycle - are polynomial-time solvable on cographs, fixed-parameter tractable (FPT) when parameterized by treewidth, but W[1]-hard when parameterized by clique-width. In contrast, Graph Isomorphism is FPT parameterized by treewidth, but for clique-width it is known to be in XP; whether it is FPT or W[1]-hard is open. This reveals a sharp tractability gap between treewidth and clique-width. In this work, we propose a new structural graph parameter, 𝒞-modular-treewidth, which lies between treewidth and clique-width. The parameter leverages modular decomposition and restricts modules to induce graphs from a fixed class 𝒞 (e.g., cographs or edgeless graphs). By exploiting true and false twins - a hallmark of cograph-like structure - our parameter allows the design of efficient algorithms for several hard problems beyond the reach of treewidth-based methods. In this work, we show that 𝒞-modular-treewidth enables efficient solutions under suitable choices of 𝒞, opening a new pathway in the parameterized complexity landscape between treewidth and clique-width. In particular we show that - When parameterized by cograph-modular-treewidth, Isomorphism admits an FPT algorithm, whereas Chromatic Number remains W[1]-hard. - When parameterized by independent-modular-treewidth, Hamiltonian Cycle and Edge Dominating Set remain W[1]-hard.
Cite as

Václav Blažej, Satyabrata Jana, M. S. Ramanujan, and Peter Strulo. Bridging Treewidth and Clique-Width via Cograph-Modular-Treewidth. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 18:1-18:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{blazej_et_al:LIPIcs.IPEC.2025.18,
  author =	{Bla\v{z}ej, V\'{a}clav and Jana, Satyabrata and Ramanujan, M. S. and Strulo, Peter},
  title =	{{Bridging Treewidth and Clique-Width via Cograph-Modular-Treewidth}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{18:1--18:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.18},
  URN =		{urn:nbn:de:0030-drops-251507},
  doi =		{10.4230/LIPIcs.IPEC.2025.18},
  annote =	{Keywords: Treewidth, Clique-width, Cograph, FPT, W\lbrack1\rbrack-hard}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.19
Tight Bounds for Connected Odd Cycle Transversal Parameterized by Clique-Width

Authors: Narek Bojikian and Stefan Kratsch

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
Recently, Bojikian and Kratsch [ICALP 2024] presented a novel approach to tackle connectivity problems parameterized by clique-width (cw), based on counting (modulo 2) the number of representations of partial solutions, while allowing for possibly multiple representations to exist for the same partial solution. Using this technique, they got a SETH-tight bound of 𝒪^*(3^{cw}) for the Steiner Tree problem, which was left open by Hegerfeld and Kratsch [ESA 2023]. We use the same technique to solve the Connected Odd Cycle Transversal problem in time 𝒪^*(12^{cw}). Moreover, we prove that our result is tight by providing a SETH-based lower bound excluding algorithms with running time 𝒪^*((12-ε)^{cw}). This answers another question of Hegerfeld and Kratsch [ESA 2023].
Cite as

Narek Bojikian and Stefan Kratsch. Tight Bounds for Connected Odd Cycle Transversal Parameterized by Clique-Width. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 19:1-19:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bojikian_et_al:LIPIcs.IPEC.2025.19,
  author =	{Bojikian, Narek and Kratsch, Stefan},
  title =	{{Tight Bounds for Connected Odd Cycle Transversal Parameterized by Clique-Width}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{19:1--19:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.19},
  URN =		{urn:nbn:de:0030-drops-251516},
  doi =		{10.4230/LIPIcs.IPEC.2025.19},
  annote =	{Keywords: Parameterized complexity, connected odd cycle transversal, clique-width}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.20
Sparse Induced Subgraphs in P₇-Free Graphs of Bounded Clique Number

Authors: Maria Chudnovsky, Jadwiga Czyżewska, Kacper Kluk, Marcin Pilipczuk, and Paweł Rzążewski

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
Many natural computational problems, including e.g. Max Weight Independent Set, Feedback Vertex Set, or Vertex Planarization, can be unified under an umbrella of finding the largest sparse induced subgraph that satisfies some property definable in CMSO₂ logic. It is believed that each problem expressible with this formalism can be solved in polynomial time in graphs that exclude a fixed path as an induced subgraph. This belief is supported by the existence of a quasipolynomial-time algorithm by Gartland, Lokshtanov, Pilipczuk, Pilipczuk, and Rzążewski [STOC 2021], and a recent polynomial-time algorithm for P₆-free graphs by Chudnovsky, McCarty, Pilipczuk, Pilipczuk, and Rzążewski [SODA 2024]. In this work we extend polynomial-time tractability of all such problems to P₇-free graphs of bounded clique number.
Cite as

Maria Chudnovsky, Jadwiga Czyżewska, Kacper Kluk, Marcin Pilipczuk, and Paweł Rzążewski. Sparse Induced Subgraphs in P₇-Free Graphs of Bounded Clique Number. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 20:1-20:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chudnovsky_et_al:LIPIcs.ISAAC.2025.20,
  author =	{Chudnovsky, Maria and Czy\.{z}ewska, Jadwiga and Kluk, Kacper and Pilipczuk, Marcin and Rz\k{a}\.{z}ewski, Pawe{\l}},
  title =	{{Sparse Induced Subgraphs in P₇-Free Graphs of Bounded Clique Number}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{20:1--20:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.20},
  URN =		{urn:nbn:de:0030-drops-249282},
  doi =		{10.4230/LIPIcs.ISAAC.2025.20},
  annote =	{Keywords: P\underlinet-free graphs, maximum weight induced subgraph, maximum weight independent set}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.3
Generalized Graph Packing Problems Parameterized by Treewidth

Authors: Barış Can Esmer and Dániel Marx

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
H-Packing is the problem of finding a maximum number of vertex-disjoint copies of H in a given graph G. H-Partition is the special case of finding a set of vertex-disjoint copies that cover each vertex of G exactly once. Our goal is to study these problems and some generalizations on bounded-treewidth graphs. The case of H being a triangle is well understood: given a tree decomposition of G having treewidth tw, the K₃-Packing problem can be solved in time 2^tw⋅ n^O(1), while Lokshtanov et al. [ACM Transactions on Algorithms 2018] showed, under the Strong Exponential-Time Hypothesis (SETH), that there is no (2-ε)^tw⋅ n^O(1) algorithm for any ε > 0 even for K₃-Partition. Similar results can be obtained for any other clique K_d for d ≥ 3. We provide generalizations in two directions: - We consider a generalization of the problem where every vertex can be used at most c times for some c ≥ 1. When H is any clique K_d with d ≥ 3, then we give upper and lower bounds showing that the optimal running time increases to (c+1)^tw⋅ n^O(1). We consider two variants depending on whether a copy of H can be used multiple times in the packing. - If H is not a clique, then the dependence of the running time on treewidth may not be even single exponential. Specifically, we show that if H is any fixed graph where not every 2-connected component is a clique, then there is no 2^o(tw log tw)⋅ n^O(1) algorithm for H-Partition, assuming the Exponential-Time Hypothesis (ETH).
Cite as

Barış Can Esmer and Dániel Marx. Generalized Graph Packing Problems Parameterized by Treewidth. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 3:1-3:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{canesmer_et_al:LIPIcs.ESA.2025.3,
  author =	{Can Esmer, Bar{\i}\c{s} and Marx, D\'{a}niel},
  title =	{{Generalized Graph Packing Problems Parameterized by Treewidth}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{3:1--3:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.3},
  URN =		{urn:nbn:de:0030-drops-244713},
  doi =		{10.4230/LIPIcs.ESA.2025.3},
  annote =	{Keywords: Graph Packing, Graph Partitioning, Parameterized Complexity, Treewidth, Pathwidth, pw-SETH, Single-Exponential Lower Bound, Slightly Superexponential Lower Bound}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.13
Tight Bounds for Some Classical Problems Parameterized by Cutwidth

Authors: Narek Bojikian, Vera Chekan, and Stefan Kratsch

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
Cutwidth is a widely studied parameter and it quantifies how well a graph can be decomposed along small edge-cuts. It complements pathwidth, which captures decomposition by small vertex separators, and it is well-known that cutwidth upper-bounds pathwidth. The SETH-tight parameterized complexity of problems on graphs of bounded pathwidth (and treewidth) has been actively studied over the past decade while for cutwidth the complexity of many classical problems remained open. For Hamiltonian Cycle, it is known that a (2+√2)^{pw} n^𝒪(1) algorithm is optimal for pathwidth under SETH [Cygan et al. JACM 2018]. Van Geffen et al. [J. Graph Algorithms Appl. 2020] and Bojikian et al. [STACS 2023] asked which running time is optimal for this problem parameterized by cutwidth. We answer this question with (1+√2)^{ctw} n^𝒪(1) by providing matching upper and lower bounds. Second, as our main technical contribution, we close the gap left by van Heck [2018] for Partition Into Triangles (and Triangle Packing) by improving both upper and lower bound and getting a tight bound of ∛{3}^{ctw} n^𝒪(1), which to our knowledge exhibits the only known tight non-integral basis apart from Hamiltonian Cycle [Cygan et al. JACM 2018] and C₄-Hitting Set [SODA 2025]. We show that the cuts inducing a disjoint union of paths of length three (unions of so-called Z-cuts) lie at the core of the complexity of the problem - usually lower-bound constructions use simpler cuts inducing either a matching or a disjoint union of bicliques. Finally, we determine the optimal running times for Max Cut (2^{ctw} n^𝒪(1)) and Induced Matching (3^{ctw} n^𝒪(1)) by providing matching lower bounds for the existing algorithms - the latter result also answers an open question for treewidth by Chaudhary and Zehavi [WG 2023].
Cite as

Narek Bojikian, Vera Chekan, and Stefan Kratsch. Tight Bounds for Some Classical Problems Parameterized by Cutwidth. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bojikian_et_al:LIPIcs.ESA.2025.13,
  author =	{Bojikian, Narek and Chekan, Vera and Kratsch, Stefan},
  title =	{{Tight Bounds for Some Classical Problems Parameterized by Cutwidth}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{13:1--13:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.13},
  URN =		{urn:nbn:de:0030-drops-244815},
  doi =		{10.4230/LIPIcs.ESA.2025.13},
  annote =	{Keywords: Parameterized complexity, cutwidth, Hamiltonian cycle, triangle packing, max cut, induced matching}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.28
Graphs with No Long Claws: An Improved Bound for the Analog of the Gyárfás' Path Argument

Authors: Romain Bourneuf, Jana Masaříková, Wojciech Nadara, and Marcin Pilipczuk

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
For a fixed integer t ⩾ 1, a (t-)long claw, denoted S_{t,t,t}, is the unique tree with three leaves, each at distance exactly t from the vertex of degree three. Majewski et al. [ICALP 2022, ACM ToCT 2024] proved an analog of the Gyárfás' path argument for S_{t,t,t}-free graphs: given an n-vertex S_{t,t,t}-free graph, one can delete neighborhoods of 𝒪(log n) vertices so that the remainder admits an extended strip decomposition (an appropriate generalization of partition into connected components) into particles of multiplicatively smaller size. In this work, we refine the argument of Majewski et al. to its arguably final form: we show that a constant number of neighborhoods suffice. The statement of Majewski et al. is one of the two pillars of a recent quasi-polynomial time algorithm for Maximum Weight Independent Set in S_{t,t,t}-free graphs [Gartland et al., STOC 2024]; our work immediately improves the quasi-polynomial function in the running time bound. Furthermore, our result significantly simplifies known polynomial-time algorithms for Maximum Weight Independent Set in S_{t,t,t}-free graphs with an additional sparsity assumption such as bounded degree or excluding a fixed biclique as a subgraph.
Cite as

Romain Bourneuf, Jana Masaříková, Wojciech Nadara, and Marcin Pilipczuk. Graphs with No Long Claws: An Improved Bound for the Analog of the Gyárfás' Path Argument. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 28:1-28:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bourneuf_et_al:LIPIcs.MFCS.2025.28,
  author =	{Bourneuf, Romain and Masa\v{r}{\'\i}kov\'{a}, Jana and Nadara, Wojciech and Pilipczuk, Marcin},
  title =	{{Graphs with No Long Claws: An Improved Bound for the Analog of the Gy\'{a}rf\'{a}s' Path Argument}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{28:1--28:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.28},
  URN =		{urn:nbn:de:0030-drops-241350},
  doi =		{10.4230/LIPIcs.MFCS.2025.28},
  annote =	{Keywords: long-claw-free graphs, extended strip decomposition, maximum weight independent set, Gy\'{a}rf\'{a}s' path, three in a tree}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.158
Restricted CSPs and F-Free Digraph Algorithmics

Authors: Santiago Guzmán-Pro and Barnaby Martin

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
In recent years, much attention has been placed on the complexity of graph homomorphism problems when the input is restricted to ℙ_k-free and ℙ_k-subgraph-free graphs. We consider the directed version of this research line, by addressing the question is it true that digraph homomorphism problems CSP(H) have a P versus NP-complete dichotomy when the input is restricted to ℙ→_k-free (resp. ℙ→_k-subgraph-free) digraphs? Our main contribution in this direction shows that if CSP(H) is NP-complete, then there is a positive integer N such that CSP(H) remains NP-hard even for ℙ→_N-subgraph-free digraphs. Moreover, CSP(H) becomes polynomial-time solvable for ℙ→_{N-1}-subgraph-free acyclic digraphs. We then verify the questions above for digraphs on three vertices and a family of smooth tournaments. We prove these results by establishing a connection between F-(subgraph)-free algorithmics and constraint satisfaction theory. On the way, we introduce restricted CSPs, i.e., problems of the form CSP(H) restricted to yes-instances of CSP(H') - these were called restricted homomorphism problems by Hell and Nešetřil. Another main result of this paper presents a P versus NP-complete dichotomy for these problems. Moreover, this complexity dichotomy is accompanied by an algebraic dichotomy in the spirit of the finite domain CSP dichotomy.
Cite as

Santiago Guzmán-Pro and Barnaby Martin. Restricted CSPs and F-Free Digraph Algorithmics. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 158:1-158:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{guzmanpro_et_al:LIPIcs.ICALP.2025.158,
  author =	{Guzm\'{a}n-Pro, Santiago and Martin, Barnaby},
  title =	{{Restricted CSPs and F-Free Digraph Algorithmics}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{158:1--158:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.158},
  URN =		{urn:nbn:de:0030-drops-235352},
  doi =		{10.4230/LIPIcs.ICALP.2025.158},
  annote =	{Keywords: Digraph homomorphisms, constraint satisfaction problems, subgraph-free algorithmics}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.41
Residue Domination in Bounded-Treewidth Graphs

Authors: Jakob Greilhuber, Philipp Schepper, and Philip Wellnitz

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
For the vertex selection problem (σ,ρ)-DomSet one is given two fixed sets σ and ρ of integers and the task is to decide whether we can select vertices of the input graph such that, for every selected vertex, the number of selected neighbors is in σ and, for every unselected vertex, the number of selected neighbors is in ρ [Telle, Nord. J. Comp. 1994]. This framework covers many fundamental graph problems such as Independent Set and Dominating Set. We significantly extend the recent result by Focke et al. [SODA 2023] to investigate the case when σ and ρ are two (potentially different) residue classes modulo m ≥ 2. We study the problem parameterized by treewidth and present an algorithm that solves in time m^tw ⋅ n^O(1) the decision, minimization and maximization version of the problem. This significantly improves upon the known algorithms where for the case m ≥ 3 not even an explicit running time is known. We complement our algorithm by providing matching lower bounds which state that there is no (m-ε)^pw ⋅ n^O(1)-time algorithm parameterized by pathwidth pw, unless SETH fails. For m = 2, we extend these bounds to the minimization version as the decision version is efficiently solvable.
Cite as

Jakob Greilhuber, Philipp Schepper, and Philip Wellnitz. Residue Domination in Bounded-Treewidth Graphs. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 41:1-41:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{greilhuber_et_al:LIPIcs.STACS.2025.41,
  author =	{Greilhuber, Jakob and Schepper, Philipp and Wellnitz, Philip},
  title =	{{Residue Domination in Bounded-Treewidth Graphs}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{41:1--41:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.41},
  URN =		{urn:nbn:de:0030-drops-228675},
  doi =		{10.4230/LIPIcs.STACS.2025.41},
  annote =	{Keywords: Parameterized Complexity, Treewidth, Generalized Dominating Set, Strong Exponential Time Hypothesis}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.85
Tree Decompositions Meet Induced Matchings: Beyond Max Weight Independent Set

Authors: Paloma T. Lima, Martin Milanič, Peter Muršič, Karolina Okrasa, Paweł Rzążewski, and Kenny Štorgel

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
For a tree decomposition 𝒯 of a graph G, by μ(𝒯) we denote the size of a largest induced matching in G all of whose edges intersect one bag of 𝒯. The induced matching treewidth of a graph G is the minimum value of μ(𝒯) over all tree decompositions 𝒯 of G. Yolov [SODA 2018] proved that for graphs of bounded induced matching treewidth, tree decompositions with bounded μ(𝒯) can be computed in polynomial time and Max Weight Independent Set can be solved in polynomial time. In this paper we explore what other problems are tractable in such classes of graphs. As our main result, we give a polynomial-time algorithm for Min Weight Feedback Vertex Set. We also provide some positive results concerning packing induced subgraphs, which in particular imply a PTAS for the problem of finding a largest induced subgraph of bounded treewidth. These results suggest that in graphs of bounded induced matching treewidth, one could find in polynomial time a maximum-weight induced subgraph of bounded treewidth satisfying a given CMSO₂ formula. We conjecture that such a result indeed holds and prove it for graphs of bounded tree-independence number, which form a rich and important family of subclasses of graphs of bounded induced matching treewidth. We complement these algorithmic results with a number of complexity and structural results concerning induced matching treewidth, including a linear relation to treewidth for graphs with bounded degree.
Cite as

Paloma T. Lima, Martin Milanič, Peter Muršič, Karolina Okrasa, Paweł Rzążewski, and Kenny Štorgel. Tree Decompositions Meet Induced Matchings: Beyond Max Weight Independent Set. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 85:1-85:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{lima_et_al:LIPIcs.ESA.2024.85,
  author =	{Lima, Paloma T. and Milani\v{c}, Martin and Mur\v{s}i\v{c}, Peter and Okrasa, Karolina and Rz\k{a}\.{z}ewski, Pawe{\l} and \v{S}torgel, Kenny},
  title =	{{Tree Decompositions Meet Induced Matchings: Beyond Max Weight Independent Set}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{85:1--85:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.85},
  URN =		{urn:nbn:de:0030-drops-211569},
  doi =		{10.4230/LIPIcs.ESA.2024.85},
  annote =	{Keywords: induced matching treewidth, tree-independence number, feedback vertex set, induced packing, algorithmic meta-theorem}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.55
Minimal Obstructions to C₅-Coloring in Hereditary Graph Classes

Authors: Jan Goedgebeur, Jorik Jooken, Karolina Okrasa, Paweł Rzążewski, and Oliver Schaudt

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
For graphs G and H, an H-coloring of G is an edge-preserving mapping from V(G) to V(H). Note that if H is the triangle, then H-colorings are equivalent to 3-colorings. In this paper we are interested in the case that H is the five-vertex cycle C₅. A minimal obstruction to C₅-coloring is a graph that does not have a C₅-coloring, but every proper induced subgraph thereof has a C₅-coloring. In this paper we are interested in minimal obstructions to C₅-coloring in F-free graphs, i.e., graphs that exclude some fixed graph F as an induced subgraph. Let P_t denote the path on t vertices, and let S_{a,b,c} denote the graph obtained from paths P_{a+1},P_{b+1},P_{c+1} by identifying one of their endvertices. We show that there is only a finite number of minimal obstructions to C₅-coloring among F-free graphs, where F ∈ {P₈, S_{2,2,1}, S_{3,1,1}} and explicitly determine all such obstructions. This extends the results of Kamiński and Pstrucha [Discr. Appl. Math. 261, 2019] who proved that there is only a finite number of P₇-free minimal obstructions to C₅-coloring, and of Dębski et al. [ISAAC 2022 Proc.] who showed that the triangle is the unique S_{2,1,1}-free minimal obstruction to C₅-coloring. We complement our results with a construction of an infinite family of minimal obstructions to C₅-coloring, which are simultaneously P_{13}-free and S_{2,2,2}-free. We also discuss infinite families of F-free minimal obstructions to H-coloring for other graphs H.
Cite as

Jan Goedgebeur, Jorik Jooken, Karolina Okrasa, Paweł Rzążewski, and Oliver Schaudt. Minimal Obstructions to C₅-Coloring in Hereditary Graph Classes. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 55:1-55:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{goedgebeur_et_al:LIPIcs.MFCS.2024.55,
  author =	{Goedgebeur, Jan and Jooken, Jorik and Okrasa, Karolina and Rz\k{a}\.{z}ewski, Pawe{\l} and Schaudt, Oliver},
  title =	{{Minimal Obstructions to C₅-Coloring in Hereditary Graph Classes}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{55:1--55:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.55},
  URN =		{urn:nbn:de:0030-drops-206110},
  doi =		{10.4230/LIPIcs.MFCS.2024.55},
  annote =	{Keywords: graph homomorphism, critical graphs, hereditary graph classes}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2023.36
Coloring and Recognizing Mixed Interval Graphs

Authors: Grzegorz Gutowski, Konstanty Junosza-Szaniawski, Felix Klesen, Paweł Rzążewski, Alexander Wolff, and Johannes Zink

Published in: LIPIcs, Volume 283, 34th International Symposium on Algorithms and Computation (ISAAC 2023)

Abstract
A mixed interval graph is an interval graph that has, for every pair of intersecting intervals, either an arc (directed arbitrarily) or an (undirected) edge. We are particularly interested in scenarios where edges and arcs are defined by the geometry of intervals. In a proper coloring of a mixed interval graph G, an interval u receives a lower (different) color than an interval v if G contains arc (u,v) (edge {u,v}). Coloring of mixed graphs has applications, for example, in scheduling with precedence constraints; see a survey by Sotskov [Mathematics, 2020]. For coloring general mixed interval graphs, we present a min {ω(G), λ(G)+1}-approximation algorithm, where ω(G) is the size of a largest clique and λ(G) is the length of a longest directed path in G. For the subclass of bidirectional interval graphs (introduced recently for an application in graph drawing), we show that optimal coloring is NP-hard. This was known for general mixed interval graphs. We introduce a new natural class of mixed interval graphs, which we call containment interval graphs. In such a graph, there is an arc (u,v) if interval u contains interval v, and there is an edge {u,v} if u and v overlap. We show that these graphs can be recognized in polynomial time, that coloring them with the minimum number of colors is NP-hard, and that there is a 2-approximation algorithm for coloring.
Cite as

Grzegorz Gutowski, Konstanty Junosza-Szaniawski, Felix Klesen, Paweł Rzążewski, Alexander Wolff, and Johannes Zink. Coloring and Recognizing Mixed Interval Graphs. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 36:1-36:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{gutowski_et_al:LIPIcs.ISAAC.2023.36,
  author =	{Gutowski, Grzegorz and Junosza-Szaniawski, Konstanty and Klesen, Felix and Rz\k{a}\.{z}ewski, Pawe{\l} and Wolff, Alexander and Zink, Johannes},
  title =	{{Coloring and Recognizing Mixed Interval Graphs}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{36:1--36:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-289-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{283},
  editor =	{Iwata, Satoru and Kakimura, Naonori},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.36},
  URN =		{urn:nbn:de:0030-drops-193388},
  doi =		{10.4230/LIPIcs.ISAAC.2023.36},
  annote =	{Keywords: Interval Graphs, Mixed Graphs, Graph Coloring}
}
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