Document

**Published in:** LIPIcs, Volume 289, 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)

We revisit the recent polynomial-time algorithm for the Max Weight Independent Set (MWIS) problem in bounded-degree graphs that do not contain a fixed graph whose every component is a subdivided claw as an induced subgraph [Abrishami, Chudnovsky, Dibek, Rzążewski, SODA 2022].
First, we show that with an arguably simpler approach we can obtain a faster algorithm with running time n^{𝒪(Δ²)}, where n is the number of vertices of the instance and Δ is the maximum degree. Then we combine our technique with known results concerning tree decompositions and provide a polynomial-time algorithm for MWIS in graphs excluding a fixed graph whose every component is a subdivided claw as an induced subgraph, and a fixed biclique as a subgraph.

Tara Abrishami, Maria Chudnovsky, Marcin Pilipczuk, and Paweł Rzążewski. Max Weight Independent Set in Sparse Graphs with No Long Claws. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 4:1-4:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{abrishami_et_al:LIPIcs.STACS.2024.4, author = {Abrishami, Tara and Chudnovsky, Maria and Pilipczuk, Marcin and Rz\k{a}\.{z}ewski, Pawe{\l}}, title = {{Max Weight Independent Set in Sparse Graphs with No Long Claws}}, booktitle = {41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)}, pages = {4:1--4:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-311-9}, ISSN = {1868-8969}, year = {2024}, volume = {289}, editor = {Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.4}, URN = {urn:nbn:de:0030-drops-197148}, doi = {10.4230/LIPIcs.STACS.2024.4}, annote = {Keywords: Max Weight Independent Set, subdivided claw, hereditary classes} }

Document

**Published in:** Dagstuhl Reports, Volume 12, Issue 11 (2023)

This report documents the program and the outcomes of Dagstuhl Seminar 22481 "Vertex Partitioning in Graphs: From Structure to Algorithms", which was held from 27 November to 2 December 2023. The report contains abstracts for presentations about recent structural and algorithmic developments for a variety of vertex partitioning problems. It also contains a collection of open problems which were posed during the seminar.

Maria Chudnovsky, Neeldhara Misra, Daniel Paulusma, Oliver Schaudt, and Akanksha Agrawal. Vertex Partitioning in Graphs: From Structure to Algorithms (Dagstuhl Seminar 22481). In Dagstuhl Reports, Volume 12, Issue 11, pp. 109-123, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@Article{chudnovsky_et_al:DagRep.12.11.109, author = {Chudnovsky, Maria and Misra, Neeldhara and Paulusma, Daniel and Schaudt, Oliver and Agrawal, Akanksha}, title = {{Vertex Partitioning in Graphs: From Structure to Algorithms (Dagstuhl Seminar 22481)}}, pages = {109--123}, journal = {Dagstuhl Reports}, ISSN = {2192-5283}, year = {2023}, volume = {12}, number = {11}, editor = {Chudnovsky, Maria and Misra, Neeldhara and Paulusma, Daniel and Schaudt, Oliver and Agrawal, Akanksha}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagRep.12.11.109}, URN = {urn:nbn:de:0030-drops-178384}, doi = {10.4230/DagRep.12.11.109}, annote = {Keywords: computational complexity, hereditary graph classes, parameterized algorithms, polynomial-time algorithms, vertex partitioning} }

Document

**Published in:** LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)

We study the Max Partial H-Coloring problem: given a graph G, find the largest induced subgraph of G that admits a homomorphism into H, where H is a fixed pattern graph without loops. Note that when H is a complete graph on k vertices, the problem reduces to finding the largest induced k-colorable subgraph, which for k = 2 is equivalent (by complementation) to Odd Cycle Transversal.
We prove that for every fixed pattern graph H without loops, Max Partial H-Coloring can be solved:
- in {P₅,F}-free graphs in polynomial time, whenever F is a threshold graph;
- in {P₅,bull}-free graphs in polynomial time;
- in P₅-free graphs in time n^𝒪(ω(G));
- in {P₆,1-subdivided claw}-free graphs in time n^𝒪(ω(G)³). Here, n is the number of vertices of the input graph G and ω(G) is the maximum size of a clique in G. Furthermore, by combining the mentioned algorithms for P₅-free and for {P₆,1-subdivided claw}-free graphs with a simple branching procedure, we obtain subexponential-time algorithms for Max Partial H-Coloring in these classes of graphs.
Finally, we show that even a restricted variant of Max Partial H-Coloring is NP-hard in the considered subclasses of P₅-free graphs, if we allow loops on H.

Maria Chudnovsky, Jason King, Michał Pilipczuk, Paweł Rzążewski, and Sophie Spirkl. Finding Large H-Colorable Subgraphs in Hereditary Graph Classes. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 35:1-35:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{chudnovsky_et_al:LIPIcs.ESA.2020.35, author = {Chudnovsky, Maria and King, Jason and Pilipczuk, Micha{\l} and Rz\k{a}\.{z}ewski, Pawe{\l} and Spirkl, Sophie}, title = {{Finding Large H-Colorable Subgraphs in Hereditary Graph Classes}}, booktitle = {28th Annual European Symposium on Algorithms (ESA 2020)}, pages = {35:1--35:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-162-7}, ISSN = {1868-8969}, year = {2020}, volume = {173}, editor = {Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.35}, URN = {urn:nbn:de:0030-drops-129019}, doi = {10.4230/LIPIcs.ESA.2020.35}, annote = {Keywords: homomorphisms, hereditary graph classes, odd cycle transversal} }

Document

**Published in:** Dagstuhl Reports, Volume 9, Issue 6 (2020)

This report documents the program and the outcomes of Dagstuhl Seminar 19271 "Graph Colouring: from Structure to Algorithm", which was held from 30 June to 5 July 2019. The report contains abstracts for presentations about recent structural and algorithmic developments for the Graph Colouring problem and variants of it. It also contains a collection of open problems on graph colouring which were posed during the seminar.

Maria Chudnovsky, Daniel Paulusma, and Oliver Schaudt. Graph Colouring: from Structure to Algorithms (Dagstuhl Seminar 19271). In Dagstuhl Reports, Volume 9, Issue 6, pp. 125-142, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@Article{chudnovsky_et_al:DagRep.9.6.125, author = {Chudnovsky, Maria and Paulusma, Daniel and Schaudt, Oliver}, title = {{Graph Colouring: from Structure to Algorithms (Dagstuhl Seminar 19271)}}, pages = {125--142}, journal = {Dagstuhl Reports}, ISSN = {2192-5283}, year = {2019}, volume = {9}, number = {6}, editor = {Chudnovsky, Maria and Paulusma, Daniel and Schaudt, Oliver}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagRep.9.6.125}, URN = {urn:nbn:de:0030-drops-114905}, doi = {10.4230/DagRep.9.6.125}, annote = {Keywords: (certifying / parameterized / polynomial-time) algorithms, computational complexity, graph colouring, hereditary graph classes} }

Document

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

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.

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)

Copy BibTex To Clipboard

@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} }

X

Feedback for Dagstuhl Publishing

Feedback submitted

Please try again later or send an E-mail