Finding Large H-Colorable Subgraphs in Hereditary Graph Classes

Loading...
Thumbnail Image

Date

2021-10-14

Authors

Chudnovsky, Maria
King, Jason
Pilipczuk, Michał
Rzążewski, Paweł
Spirkl, Sophie

Advisor

Journal Title

Journal ISSN

Volume Title

Publisher

Society for Industrial and Applied Mathematics

Abstract

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 nO(ω(G)); and in {P6,1−subdividedclaw}-free graphs in time nO(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−subdividedclaw}-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.

Description

“First Published in SIAM Journal on Discrete Mathematics in 35, 4, 2021, published by the Society for Industrial and Applied Mathematics (SIAM)” and the copyright notice as stated in the article itself (e.g., “Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.”')

Keywords

odd cycle transversal, graph homomorphism, P5-free graphs

LC Subject Headings

Citation