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List-k-Coloring H-Free Graphs for All k > 4

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LkC_rP3_free_graphs.pdf (386.78 KB)

Date

2024-05-14

Authors

Chudnovsky, Maria
Hajebi, Sepehr
Spirkl, Sophie

Journal Title

Journal ISSN

Volume Title

Publisher

Springer

Abstract

Given an integer k > 4 and a graph H, we prove that, assuming P =/ NP, the LIST-k-COLORING PROBLEM restricted to H-free graphs can be solved in polynomial time if and only if either every component of H is a path on at most three vertices, or removing the isolated vertices of H leaves an induced subgraph of the five-vertex path. In fact, the "if" implication holds for all k>_ 1.

Description

This is a post-peer-review, pre-copyedit version of an article published in Combinatorica. The final authenticated version is available online at: https://doi.org/10.1007/s00493-024-00106-2

Keywords

coloring, list-coloring, induced subgraphs, polynomial-time algorithms

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Citation

URI

https://doi.org/10.1007/s00493-024-00106-2
 http://hdl.handle.net/10012/20595

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Waterloo Research