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Complexity of Ck-coloring in hereditary classes of graphs

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dc.contributor.authorChudnovsky, Maria
dc.contributor.authorHuang, Shenwei
dc.contributor.authorRzazewski, Pawel
dc.contributor.authorSpirkl, Sophie
dc.contributor.authorZhong, Mingxian
dc.date.accessioned2023-03-31T19:27:26Z
dc.date.available2023-03-31T19:27:26Z
dc.date.issued2023-06
dc.description.abstractFor 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 ∈ E(G) it holds that f(u)f(v) ∈ 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 Pt-free graphs. We show that for every odd k ≥ 5, the Ck-Coloring problem, even in the list variant, can be solved in polynomial time in P9 free graphs. The algorithm extends to the list version of Ck-Coloring, where k ≥ 10 is an even number. On the other hand, we prove that if some component of F is not a subgraph of a subdivided claw, then the following problems are NP-complete in F-free graphs: a) the precoloring extension version of Ck-Coloring for every odd k ≥ 5; b) the list version of Ck-Coloring for every even k ≥ 6.en
dc.description.sponsorshipNSF, grant DMS-1763817 || U.S. Army Research Laboratory and the U.S. Army Research Office, Grant W911NF-16-1-0404 || National Natural Science Foundation of China, 12171256 || Polish National Science Centre, Grant 2018/31/D/ST6/00062 || National Science Foundation, DMS-1802201.en
dc.identifier.urihttps://doi.org/10.1016/j.ic.2023.105015
dc.identifier.urihttp://hdl.handle.net/10012/19243
dc.language.isoenen
dc.publisherElsevieren
dc.relation.ispartofseriesInformation and Computation;105015
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subjectgraph coloringen
dc.subjecthomomorphismen
dc.subjectcomputational complexityen
dc.subjecthereditary graph classesen
dc.titleComplexity of Ck-coloring in hereditary classes of graphsen
dc.typeArticleen
dcterms.bibliographicCitationChudnovsky, M., Huang, S., Rzążewski, P., Spirkl, S., & Zhong, M. (2023). Complexity of C-coloring in hereditary classes of graphs. Information and Computation, 292, 105015. https://doi.org/10.1016/j.ic.2023.105015en
uws.contributor.affiliation1Faculty of Mathematicsen
uws.contributor.affiliation2Combinatorics and Optimizationen
uws.peerReviewStatusRevieweden
uws.scholarLevelFacultyen
uws.typeOfResourceTexten

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