12 Search Results for "Lozin, Vadim V."

Document
DOI: 10.4230/LIPIcs.WG.2026.14
Graph Classes Closed Under Self-Intersection

Authors: Konrad K. Dabrowski, Vadim Lozin, Martin Milanič, Andrea Munaro, Daniël Paulusma, and Viktor Zamaraev

Published in: LIPIcs, Volume 376, 52nd International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2026)

Abstract
A graph class is monotone if it is closed under taking subgraphs. A monotone class defined by finitely many obstructions has bounded treewidth if and only if one of the obstructions is a tripod, i.e. a disjoint union of subdivided claws and paths. This dichotomy also characterizes exactly those monotone graph classes for which many NP-hard graph problems admit polynomial-time algorithms. These dichotomies do not extend to the universe of all hereditary classes. This leads to the question of whether we can extend known dichotomies for monotone classes to larger families of hereditary classes. We answer this question affirmatively by considering the family of hereditary graph classes closed under self-intersection. This family is known to be located strictly between the monotone and hereditary classes. We prove a new structural characterization of graphs in self-intersection-closed classes excluding a tripod. In contrast to monotone classes excluding a tripod, these classes do not necessarily have bounded treewidth; in fact, they do not even need to be sparse. We use our characterization to give a complete dichotomy for Maximum Independent Set, and its weighted variant, on self-intersection-closed classes defined by finitely many obstructions: these problems are in P if the class excludes a tripod and NP-hard otherwise. Our dichotomy generalizes several known results on Maximum Independent Set in the literature. We also apply our characterization to obtain a dichotomy for Maximum Induced Matching on self-intersection-closed classes of bipartite graphs defined by finitely many obstructions, and for Satisfiability and Counting Satisfiability on self-intersection-closed classes of (bipartite) incidence graphs defined by finitely many obstructions. Finally, we use our characterization to obtain a dichotomy for boundedness of clique-width for self-intersection-closed classes of bipartite graphs defined by finitely many obstructions.
Cite as

Konrad K. Dabrowski, Vadim Lozin, Martin Milanič, Andrea Munaro, Daniël Paulusma, and Viktor Zamaraev. Graph Classes Closed Under Self-Intersection. In 52nd International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 376, pp. 14:1-14:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{dabrowski_et_al:LIPIcs.WG.2026.14,
  author =	{Dabrowski, Konrad K. and Lozin, Vadim and Milani\v{c}, Martin and Munaro, Andrea and Paulusma, Dani\"{e}l and Zamaraev, Viktor},
  title =	{{Graph Classes Closed Under Self-Intersection}},
  booktitle =	{52nd International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2026)},
  pages =	{14:1--14:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-430-7},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{376},
  editor =	{Goedgebeur, Jan and Rz\k{a}\.{z}ewski, Pawe{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WG.2026.14},
  URN =		{urn:nbn:de:0030-drops-261801},
  doi =		{10.4230/LIPIcs.WG.2026.14},
  annote =	{Keywords: graph classes, self-intersection closed, dichotomy, independent set, clique-width, treewidth}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.9
QPTAS for MWIS and Finding Large Sparse Induced Subgraphs in Graphs with Few Independent Long Holes

Authors: Édouard Bonnet, Jadwiga Czyżewska, Tomáš Masařík, Marcin Pilipczuk, and Paweł Rzążewski

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract
We present a quasipolynomial-time approximation scheme (QPTAS) for the Maximum Independent Set (MWIS) in graphs with a bounded number of pairwise vertex-disjoint and non-adjacent long induced cycles. More formally, for every fixed s and t, we show a QPTAS for MWIS in graphs that exclude sC_t as an induced minor. Combining this with known results, we obtain a QPTAS for the problem of finding a largest induced subgraph of bounded treewidth with given hereditary property definable in Counting Monadic Second Order Logic, in the same classes of graphs. This is a step towards a conjecture of Gartland and Lokshtanov which asserts that for any planar graph H, graphs that exclude H as an induced minor admit a polynomial-time algorithm for the latter problem. This conjecture is notoriously open and even its weaker variants are confirmed only for very restricted graphs H.
Cite as

Édouard Bonnet, Jadwiga Czyżewska, Tomáš Masařík, Marcin Pilipczuk, and Paweł Rzążewski. QPTAS for MWIS and Finding Large Sparse Induced Subgraphs in Graphs with Few Independent Long Holes. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 9:1-9:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{bonnet_et_al:LIPIcs.SWAT.2026.9,
  author =	{Bonnet, \'{E}douard and Czy\.{z}ewska, Jadwiga and Masa\v{r}{\'\i}k, Tom\'{a}\v{s} and Pilipczuk, Marcin and Rz\k{a}\.{z}ewski, Pawe{\l}},
  title =	{{QPTAS for MWIS and Finding Large Sparse Induced Subgraphs in Graphs with Few Independent Long Holes}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{9:1--9:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.9},
  URN =		{urn:nbn:de:0030-drops-260454},
  doi =		{10.4230/LIPIcs.SWAT.2026.9},
  annote =	{Keywords: independent set, long holes, QPTAS, induced subgraphs}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.73
Colouring Probe H-Free Graphs

Authors: Daniël Paulusma, Johannes Rauch, and Erik Jan van Leeuwen

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
The NP-complete problems Colouring and k-Colouring (k ≥ 3) are well studied on H-free graphs, i.e., graphs that do not contain some fixed graph H as an induced subgraph. We research to what extent the known polynomial-time algorithms for H-free graphs can be generalized if we only know some of the edges of the input graph. We do this by considering the classical probe graph model introduced in the early nineties. For a graph H, a partitioned probe H-free graph (G,P,N) consists of a graph G = (V,E), together with a set P ⊆ V of probes and an independent set N = V ⧵ P of non-probes, such that G+F is H-free for some edge set F ⊆ binom(N,2). We show the following: - We fully classify Colouring on partitioned probe H-free graphs and show that the obtained complexity dichotomy differs from the known dichotomy of Colouring for H-free graphs. - We fully classify 3-Colouring on partitioned probe P_t-free graphs: we prove polynomial-time solvability for t ≤ 5 and NP-completeness for t ≥ 6. In contrast, 3-Colouring on P_t-free graphs is known to be polynomial-time solvable for t ≤ 7 and quasi-polynomial-time solvable for t ≥ 8. Our main result is our polynomial-time algorithm for 3-Colouring on partitioned P₅-free graphs. For this result, and also for all our other polynomial-time results, we do not need to know the edge set F; we only need to know its existence. Moreover, the class of probe P₅-free graphs includes not only paths of arbitrary length but even all bipartite graphs and is much richer than the class of P₅-free graphs. The latter is also evidenced by the fact that there exist graph problems, such as Matching Cut, that are known to be polynomial-time solvable for P₅-free graphs but NP-complete for partitioned probe P₅-free graphs. In particular, unlike the class of 3-colourable P₅-free graphs, the class of 3-colourable probe P₅-free graphs has unbounded mim-width. Hence, our polynomial-time result for 3-Colouring for probe P₅-free graphs suggests that there may be another, deeper overarching reason why 3-Colouring is polynomial-time solvable for P₅-free graphs.
Cite as

Daniël Paulusma, Johannes Rauch, and Erik Jan van Leeuwen. Colouring Probe H-Free Graphs. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 73:1-73:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{paulusma_et_al:LIPIcs.STACS.2026.73,
  author =	{Paulusma, Dani\"{e}l and Rauch, Johannes and van Leeuwen, Erik Jan},
  title =	{{Colouring Probe H-Free Graphs}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{73:1--73:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle 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.2026.73},
  URN =		{urn:nbn:de:0030-drops-255621},
  doi =		{10.4230/LIPIcs.STACS.2026.73},
  annote =	{Keywords: colouring, probe graph, forbidden induced subgraph, complexity dichotomy}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.74
List Coloring Ordered Graphs with Forbidden Induced Subgraphs

Authors: Marta Piecyk and Paweł Rzążewski

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
In the List k-Coloring problem we are given a graph whose every vertex is equipped with a list, which is a subset of {1,…,k}. We need to decide if G admits a proper coloring, where every vertex receives a color from its list. The complexity of the problem in classes defined by forbidding induced subgraphs is a widely studied topic in algorithmic graph theory. Recently, Hajebi, Li, and Spirkl [SIAM J. Discr. Math. 38 (2024)] initiated the study of List 3-Coloring in ordered graphs, i.e., graphs with fixed linear ordering of vertices. Forbidding ordered induced subgraphs allows us to investigate the boundary of tractability more closely. We continue this direction of research, focusing mostly on the case of List 4-Coloring. We present several algorithmic and hardness results, which altogether provide an almost complete dichotomy for classes defined by forbidding one fixed ordered graph: our investigations leave one minimal open case.
Cite as

Marta Piecyk and Paweł Rzążewski. List Coloring Ordered Graphs with Forbidden Induced Subgraphs. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 74:1-74:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{piecyk_et_al:LIPIcs.STACS.2026.74,
  author =	{Piecyk, Marta and Rz\k{a}\.{z}ewski, Pawe{\l}},
  title =	{{List Coloring Ordered Graphs with Forbidden Induced Subgraphs}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{74:1--74:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle 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.2026.74},
  URN =		{urn:nbn:de:0030-drops-255634},
  doi =		{10.4230/LIPIcs.STACS.2026.74},
  annote =	{Keywords: coloring, ordered graphs, forbidden induced subgraphs}
}
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)

Copy BibTex To Clipboard

@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.2025.40
Maximum List r-Colorable Induced Subgraphs in kP₃-Free Graphs

Authors: Esther Galby, Paloma T. Lima, Andrea Munaro, and Amir Nikabadi

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

Abstract
We show that, for every fixed positive integers r and k, Max-Weight List r-Colorable Induced Subgraph admits a polynomial-time algorithm on kP₃-free graphs. This problem is a common generalization of Max-Weight Independent Set, Odd Cycle Transversal and List r-Coloring, among others. Our result has several consequences. First, it implies that, for every fixed r ≥ 5, assuming 𝖯 ≠ NP, Max-Weight List r-Colorable Induced Subgraph is polynomial-time solvable on H-free graphs if and only if H is an induced subgraph of either kP₃ or P₅+kP₁, for some k ≥ 1. Second, it makes considerable progress toward a complexity dichotomy for Odd Cycle Transversal on H-free graphs, allowing to answer a question of Agrawal, Lima, Lokshtanov, Rzążewski, Saurabh, and Sharma [ACM Trans. Algorithms 2025]. Third, it gives a short and self-contained proof of the known result of Chudnovsky, Hajebi, and Spirkl [Combinatorica 2024] that List r-Coloring on kP₃-free graphs is polynomial-time solvable for every fixed r and k. We also consider two natural distance-d generalizations of Max-Weight Independent Set and List r-Coloring and provide polynomial-time algorithms on kP₃-free graphs for every fixed integers r, k, and d ≥ 6.
Cite as

Esther Galby, Paloma T. Lima, Andrea Munaro, and Amir Nikabadi. Maximum List r-Colorable Induced Subgraphs in kP₃-Free Graphs. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 40:1-40:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{galby_et_al:LIPIcs.ESA.2025.40,
  author =	{Galby, Esther and Lima, Paloma T. and Munaro, Andrea and Nikabadi, Amir},
  title =	{{Maximum List r-Colorable Induced Subgraphs in kP₃-Free Graphs}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{40:1--40:13},
  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.2025.40},
  URN =		{urn:nbn:de:0030-drops-245086},
  doi =		{10.4230/LIPIcs.ESA.2025.40},
  annote =	{Keywords: Hereditary classes, list coloring, odd cycle transversal, independent set}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.70
Labelled Well Quasi Ordered Classes of Bounded Linear Clique-Width

Authors: Aliaume Lopez

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

Abstract
We construct an algorithm that inputs an MSO-interpretation from finite words to graphs, and decides if there exists a k ∈ ℕ such that the class of graphs induced by the interpretation is not well-quasi-ordered by the induced subgraph relation when vertices are freely labelled using {1, …, k}. In case no such k exists, we also prove that the class of graphs is not well-quasi-ordered by the induced subgraph relation when vertices are freely labelled using any well-quasi-ordered set of labels. As a byproduct of our analysis, we prove that for classes of bounded linear clique-width, a weak version of a conjecture by Pouzet holds.
Cite as

Aliaume Lopez. Labelled Well Quasi Ordered Classes of Bounded Linear Clique-Width. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 70:1-70:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{lopez:LIPIcs.MFCS.2025.70,
  author =	{Lopez, Aliaume},
  title =	{{Labelled Well Quasi Ordered Classes of Bounded Linear Clique-Width}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{70:1--70:17},
  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.2025.70},
  URN =		{urn:nbn:de:0030-drops-241773},
  doi =		{10.4230/LIPIcs.MFCS.2025.70},
  annote =	{Keywords: well-quasi-ordering, linear clique-width, MSO transduction, automata theory}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.SAND.2025.22
Brief Announcement: Exploring Word-Representable Temporal Graphs

Authors: Duncan Adamson

Published in: LIPIcs, Volume 330, 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)

Abstract
Word-representable graphs are a subset of graphs that may be represented by a word w over an alphabet composed of the vertices in the graph. In such graphs, an edge exists if and only if the occurrences of the corresponding vertices alternate in the word w. We generalise this notion to temporal graphs, constructing timesteps by partitioning the word into factors (contiguous subwords) such that no factor contains more than one copy of any given symbol. With this definition, we study the problem of exploration, asking for the fastest schedule such that a given agent may explore all n vertices of the graph. We show that if the corresponding temporal graph is connected in every timestep, we may explore the graph in 2δ n timesteps, where δ is the lowest degree of any vertex in the graph. In general, we show that, for any temporal graph represented by a word of length at least n(2dn + d), with a connected underlying graph, the full graph can be explored in 2 d n timesteps, where d is the diameter of the graph.
Cite as

Duncan Adamson. Brief Announcement: Exploring Word-Representable Temporal Graphs. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 22:1-22:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{adamson:LIPIcs.SAND.2025.22,
  author =	{Adamson, Duncan},
  title =	{{Brief Announcement: Exploring Word-Representable Temporal Graphs}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{22:1--22:6},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-368-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{330},
  editor =	{Meeks, Kitty and Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.22},
  URN =		{urn:nbn:de:0030-drops-230755},
  doi =		{10.4230/LIPIcs.SAND.2025.22},
  annote =	{Keywords: Temporal Graphs, Word-Representable Graphs}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.36
MaxMin Separation Problems: FPT Algorithms for st-Separator and Odd Cycle Transversal

Authors: Ajinkya Gaikwad, Hitendra Kumar, Soumen Maity, Saket Saurabh, and Roohani Sharma

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

Abstract
In this paper, we study the parameterized complexity of the MaxMin versions of two fundamental separation problems: Maximum Minimal st-Separator and Maximum Minimal Odd Cycle Transversal (OCT), both parameterized by the solution size. In the Maximum Minimal st-Separator problem, given a graph G, two distinct vertices s and t and a positive integer k, the goal is to determine whether there exists a minimal st-separator in G of size at least k. Similarly, the Maximum Minimal OCT problem seeks to determine if there exists a minimal set of vertices whose deletion results in a bipartite graph, and whose size is at least k. We demonstrate that both problems are fixed-parameter tractable parameterized by k. Our FPT algorithm for Maximum Minimal st-Separator answers the open question by Hanaka, Bodlaender, van der Zanden & Ono [TCS 2019]. One unique insight from this work is the following. We use the meta-result of Lokshtanov, Ramanujan, Saurabh & Zehavi [ICALP 2018] that enables us to reduce our problems to highly unbreakable graphs. This is interesting, as an explicit use of the recursive understanding and randomized contractions framework of Chitnis, Cygan, Hajiaghayi, Pilipczuk & Pilipczuk [SICOMP 2016] to reduce to the highly unbreakable graphs setting (which is the result that Lokshtanov et al. tries to abstract out in their meta-theorem) does not seem obvious because certain "extension" variants of our problems are W[1]-hard.
Cite as

Ajinkya Gaikwad, Hitendra Kumar, Soumen Maity, Saket Saurabh, and Roohani Sharma. MaxMin Separation Problems: FPT Algorithms for st-Separator and Odd Cycle Transversal. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 36:1-36:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{gaikwad_et_al:LIPIcs.STACS.2025.36,
  author =	{Gaikwad, Ajinkya and Kumar, Hitendra and Maity, Soumen and Saurabh, Saket and Sharma, Roohani},
  title =	{{MaxMin Separation Problems: FPT Algorithms for st-Separator and Odd Cycle Transversal}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{36:1--36:21},
  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.2025.36},
  URN =		{urn:nbn:de:0030-drops-228622},
  doi =		{10.4230/LIPIcs.STACS.2025.36},
  annote =	{Keywords: Parameterized Complexity, FPT, MaxMin problems, Maximum Minimal st-separator, Maximum Minimal Odd Cycle Transversal, Unbreakable Graphs, CMSO, Long Induced Odd Cycles, Sunflower Lemma}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.21
Adjacency Labeling Schemes for Small Classes

Authors: Édouard Bonnet, Julien Duron, John Sylvester, and Viktor Zamaraev

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
A graph class admits an implicit representation if, for every positive integer n, its n-vertex graphs have a O(log n)-bit (adjacency) labeling scheme, i.e., their vertices can be labeled by binary strings of length O(log n) such that the presence of an edge between any pair of vertices can be deduced solely from their labels. The famous Implicit Graph Conjecture posited that every hereditary (i.e., closed under taking induced subgraphs) factorial (i.e., containing 2^O(n log n) n-vertex graphs) class admits an implicit representation. The conjecture was recently refuted [Hatami and Hatami, FOCS '22], and does not even hold among monotone (i.e., closed under taking subgraphs) factorial classes [Bonnet et al., ICALP '24]. However, monotone small (i.e., containing at most n! cⁿ many n-vertex graphs for some constant c) classes do admit implicit representations. This motivates the Small Implicit Graph Conjecture: Every hereditary small class admits an O(log n)-bit labeling scheme. We provide evidence supporting the Small Implicit Graph Conjecture. First, we show that every small weakly sparse (i.e., excluding some fixed bipartite complete graph as a subgraph) class has an implicit representation. This is a consequence of the following fact of independent interest proved in the paper: Every weakly sparse small class has bounded expansion (hence, in particular, bounded degeneracy). Second, we show that every hereditary small class admits an O(log³ n)-bit labeling scheme, which provides a substantial improvement of the best-known polynomial upper bound of n^(1-ε) on the size of adjacency labeling schemes for such classes. This is a consequence of another fact of independent interest proved in the paper: Every small class has neighborhood complexity O(n log n).
Cite as

Édouard Bonnet, Julien Duron, John Sylvester, and Viktor Zamaraev. Adjacency Labeling Schemes for Small Classes. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 21:1-21:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{bonnet_et_al:LIPIcs.ITCS.2025.21,
  author =	{Bonnet, \'{E}douard and Duron, Julien and Sylvester, John and Zamaraev, Viktor},
  title =	{{Adjacency Labeling Schemes for Small Classes}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{21:1--21:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.21},
  URN =		{urn:nbn:de:0030-drops-226493},
  doi =		{10.4230/LIPIcs.ITCS.2025.21},
  annote =	{Keywords: Adjacency labeling, degeneracy, weakly sparse classes, small classes, implicit graph conjecture}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.5
Colouring (P_r+P_s)-Free Graphs

Authors: Tereza Klimošová, Josef Malík, Tomáš Masařík, Jana Novotná, Daniël Paulusma, and Veronika Slívová

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
The k-Colouring problem is to decide if the vertices of a graph can be coloured with at most k colours for a fixed integer k such that no two adjacent vertices are coloured alike. If each vertex u must be assigned a colour from a prescribed list L(u) subseteq {1,...,k}, then we obtain the List k-Colouring problem. A graph G is H-free if G does not contain H as an induced subgraph. We continue an extensive study into the complexity of these two problems for H-free graphs. We prove that List 3-Colouring is polynomial-time solvable for (P_2+P_5)-free graphs and for (P_3+P_4)-free graphs. Combining our results with known results yields complete complexity classifications of 3-Colouring and List 3-Colouring on H-free graphs for all graphs H up to seven vertices. We also prove that 5-Colouring is NP-complete for (P_3+P_5)-free graphs.
Cite as

Tereza Klimošová, Josef Malík, Tomáš Masařík, Jana Novotná, Daniël Paulusma, and Veronika Slívová. Colouring (P_r+P_s)-Free Graphs. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 5:1-5:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{klimosova_et_al:LIPIcs.ISAAC.2018.5,
  author =	{Klimo\v{s}ov\'{a}, Tereza and Mal{\'\i}k, Josef and Masa\v{r}{\'\i}k, Tom\'{a}\v{s} and Novotn\'{a}, Jana and Paulusma, Dani\"{e}l and Sl{\'\i}vov\'{a}, Veronika},
  title =	{{Colouring (P\underliner+P\underlines)-Free Graphs}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{5:1--5:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.5},
  URN =		{urn:nbn:de:0030-drops-99533},
  doi =		{10.4230/LIPIcs.ISAAC.2018.5},
  annote =	{Keywords: vertex colouring, H-free graph, linear forest}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2017.73
Clique-Width for Graph Classes Closed under Complementation

Authors: Alexandre Blanché, Konrad K. Dabrowski, Matthew Johnson, Vadim V. Lozin, Daniël Paulusma, and Viktor Zamaraev

Published in: LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)

Abstract
Clique-width is an important graph parameter due to its algorithmic and structural properties. A graph class is hereditary if it can be characterized by a (not necessarily finite) set H of forbidden induced subgraphs. We initiate a systematic study into the boundedness of clique-width of hereditary graph classes closed under complementation. First, we extend the known classification for the |H|=1 case by classifying the boundedness of clique-width for every set H of self-complementary graphs. We then completely settle the |H|=2 case. In particular, we determine one new class of (H1, complement of H1)-free graphs of bounded clique-width (as a side effect, this leaves only six classes of (H1, H2)-free graphs, for which it is not known whether their clique-width is bounded). Once we have obtained the classification of the |H|=2 case, we research the effect of forbidding self-complementary graphs on the boundedness of clique-width. Surprisingly, we show that for a set F of self-complementary graphs on at least five vertices, the classification of the boundedness of clique-width for ({H1, complement of H1} + F)-free graphs coincides with the one for the |H|=2 case if and only if F does not include the bull (the only non-empty self-complementary graphs on fewer than five vertices are P_1 and P_4, and P_4-free graphs have clique-width at most 2). Finally, we discuss the consequences of our results for COLOURING.
Cite as

Alexandre Blanché, Konrad K. Dabrowski, Matthew Johnson, Vadim V. Lozin, Daniël Paulusma, and Viktor Zamaraev. Clique-Width for Graph Classes Closed under Complementation. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 73:1-73:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{blanche_et_al:LIPIcs.MFCS.2017.73,
  author =	{Blanch\'{e}, Alexandre and Dabrowski, Konrad K. and Johnson, Matthew and Lozin, Vadim V. and Paulusma, Dani\"{e}l and Zamaraev, Viktor},
  title =	{{Clique-Width for Graph Classes Closed under Complementation}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{73:1--73:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.73},
  URN =		{urn:nbn:de:0030-drops-80756},
  doi =		{10.4230/LIPIcs.MFCS.2017.73},
  annote =	{Keywords: clique-width, self-complementary graph, forbidden induced subgraph}
}
  • Refine by Type
  • 12 Document/PDF
  • 9 Document/HTML

  • Refine by Publication Year
  • 4 2026
  • 6 2025
  • 1 2018
  • 1 2017

  • Refine by Author
  • 4 Paulusma, Daniël
  • 3 Rzążewski, Paweł
  • 3 Zamaraev, Viktor
  • 2 Bonnet, Édouard
  • 2 Czyżewska, Jadwiga
  • Show More...

  • Refine by Series/Journal
  • 12 LIPIcs

  • Refine by Classification
  • 4 Mathematics of computing → Graph theory
  • 3 Mathematics of computing → Graph algorithms
  • 3 Theory of computation → Graph algorithms analysis
  • 2 Mathematics of computing → Graph coloring
  • 2 Theory of computation → Problems, reductions and completeness
  • Show More...

  • Refine by Keyword
  • 3 independent set
  • 2 clique-width
  • 2 forbidden induced subgraph
  • 1 Adjacency labeling
  • 1 CMSO
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact