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DOI: 10.4230/LIPIcs.ESA.2019.31
URN: urn:nbn:de:0030-drops-111529
URL: https://drops.dagstuhl.de/opus/volltexte/2019/11152/
Chudnovsky, Maria ; Huang, Shenwei ; Rzazewski, Pawel ; Spirkl, Sophie ; Zhong, Mingxian
Complexity of C_k-Coloring in Hereditary Classes of Graphs
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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.
BibTeX - Entry
@InProceedings{chudnovsky_et_al:LIPIcs:2019:11152,
author = {Maria Chudnovsky and Shenwei Huang and Pawel Rzazewski and Sophie Spirkl and Mingxian Zhong},
title = {{Complexity of C_k-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 = {Michael A. Bender and Ola Svensson and Grzegorz Herman},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/11152},
URN = {urn:nbn:de:0030-drops-111529},
doi = {10.4230/LIPIcs.ESA.2019.31},
annote = {Keywords: homomorphism, hereditary class, computational complexity, forbidden induced subgraph}
}
| Keywords: | homomorphism, hereditary class, computational complexity, forbidden induced subgraph | |
| Seminar: | 27th Annual European Symposium on Algorithms (ESA 2019) | |
| Issue date: | 2019 | |
| Date of publication: | 06.09.2019 |
