eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-09-06
31:1
31:15
10.4230/LIPIcs.ESA.2019.31
article
Complexity of C_k-Coloring in Hereditary Classes of Graphs
Chudnovsky, Maria
1
Huang, Shenwei
2
Rzążewski, Paweł
3
Spirkl, Sophie
4
Zhong, Mingxian
5
Princeton University, Princeton, NJ 08544, USA
College of Computer Science, Nankai University, Tianjin 300350, China
Faculty of Mathematics and Information Science, Warsaw University of Technology, Warsaw, Poland
Rutgers University, Piscataway, NJ 08854, USA
Lehman College, CUNY, Bronx, NY 10468, USA
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol144-esa2019/LIPIcs.ESA.2019.31/LIPIcs.ESA.2019.31.pdf
homomorphism
hereditary class
computational complexity
forbidden induced subgraph