5 Search Results for "Huang, Shenwei"

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)

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@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)

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@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.ESA.2019.31
Complexity of C_k-Coloring in Hereditary Classes of Graphs

Authors: Maria Chudnovsky, Shenwei Huang, Paweł Rzążewski, Sophie Spirkl, and Mingxian Zhong

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract
For a graph F, a graph G is F-free if it does not contain an induced subgraph isomorphic to F. For two graphs G and H, an H-coloring of G is a mapping f:V(G) -> V(H) such that for every edge uv in E(G) it holds that f(u)f(v)in E(H). We are interested in the complexity of the problem H-Coloring, which asks for the existence of an H-coloring of an input graph G. In particular, we consider H-Coloring of F-free graphs, where F is a fixed graph and H is an odd cycle of length at least 5. This problem is closely related to the well known open problem of determining the complexity of 3-Coloring of P_t-free graphs. We show that for every odd k >= 5 the C_k-Coloring problem, even in the precoloring-extension variant, can be solved in polynomial time in P_9-free graphs. On the other hand, we prove that the extension version of C_k-Coloring is NP-complete for F-free graphs whenever some component of F is not a subgraph of a subdivided claw.
Cite as

Maria Chudnovsky, Shenwei Huang, Paweł Rzążewski, Sophie Spirkl, and Mingxian Zhong. Complexity of C_k-Coloring in Hereditary Classes of Graphs. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 31:1-31:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{chudnovsky_et_al:LIPIcs.ESA.2019.31,
  author =	{Chudnovsky, Maria and Huang, Shenwei and Rz\k{a}\.{z}ewski, Pawe{\l} and Spirkl, Sophie and Zhong, Mingxian},
  title =	{{Complexity of C\underlinek-Coloring in Hereditary Classes of Graphs}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{31:1--31:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola 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.2019.31},
  URN =		{urn:nbn:de:0030-drops-111529},
  doi =		{10.4230/LIPIcs.ESA.2019.31},
  annote =	{Keywords: homomorphism, hereditary class, computational complexity, forbidden induced subgraph}
}
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)

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@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.STACS.2018.35
Colouring Square-Free Graphs without Long Induced Paths

Authors: Serge Gaspers, Shenwei Huang, and Daniel Paulusma

Published in: LIPIcs, Volume 96, 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)

Abstract
The Colouring problem is to decide if the vertices of a graph can be coloured with at most k colours for a given integer k such that no two adjacent vertices are coloured alike. The complexity of Colouring is fully understood for graph classes characterized by one forbidden induced subgraph H. Despite a huge body of existing work, there are still major complexity gaps if two induced subgraphs H_1 and H_2 are forbidden. We let H_1 be the s-vertex cycle C_s and H_2 be the t-vertex path P_t. We show that Colouring is polynomial-time solvable for s=4 and t<=6, which unifies several known results for Colouring on (H_1,H_2)-free graphs. Our algorithm is based on a novel decomposition theorem for (C_4,P_6)-free graphs without clique cutsets into homogeneous pairs of sets and a new framework for bounding the clique-width of a graph by the clique-width of its subgraphs induced by homogeneous pairs of sets. To apply this framework, we also need to use divide-and-conquer to bound the clique-width of subgraphs induced by homogeneous pairs of sets. To complement our positive result we also prove that Colouring is NP-complete for s=4 and t>=9, which is the first hardness result on Colouring for (C_4,P_t)-free graphs.
Cite as

Serge Gaspers, Shenwei Huang, and Daniel Paulusma. Colouring Square-Free Graphs without Long Induced Paths. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 35:1-35:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{gaspers_et_al:LIPIcs.STACS.2018.35,
  author =	{Gaspers, Serge and Huang, Shenwei and Paulusma, Daniel},
  title =	{{Colouring Square-Free Graphs without Long Induced Paths}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{35:1--35:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-062-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{96},
  editor =	{Niedermeier, Rolf and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018.35},
  URN =		{urn:nbn:de:0030-drops-84922},
  doi =		{10.4230/LIPIcs.STACS.2018.35},
  annote =	{Keywords: graph colouring, hereditary graph class, clique-width, cycle, path}
}
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