Complexity of Ck-Coloring in Hereditary Classes of Graphs
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Date
2019
Authors
Chudnovsky, Maria
Huang, Shenwei
Rzążewski, Paweł
Spirkl, Sophie
Zhong, Mingxian
Journal Title
Journal ISSN
Volume Title
Publisher
Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik
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 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 precoloring-extension
variant, can be solved in polynomial time in P9-free graphs. On the other hand, we prove that the
extension version of Ck-Coloring is NP-complete for F-free graphs whenever some component of
F is not a subgraph of a subdivided claw.
Description
Keywords
homomorphism, hereditary class, computational complexity, forbidden induced subgraph