Maximum Partial List H-Coloring on P_5-free graphs in polynomial time
Data Structures and Algorithms
2026-03-06 v2 Computational Complexity
Abstract
In this article we show that Maximum Partial List H-Coloring is polynomial-time solvable on P_5-free graphs for every fixed graph H. In particular, this implies that Maximum k-Colorable Subgraph is polynomial-time solvable on P_5-free graphs. This answers an open question from Agrawal, Lima, Lokshtanov, Saurabh & Sharma [SODA 2024]. This also improves the -time algorithm for Maximum Partial H-Coloring by Chudnovsky, King, Pilipczuk, Rz\k{a}\.{z}ewski & Spirkl [SIDMA 2021] to polynomial-time algorithm.
Cite
@article{arxiv.2410.21569,
title = {Maximum Partial List H-Coloring on P_5-free graphs in polynomial time},
author = {Daniel Lokshtanov and Paweł Rzążewski and Saket Saurabh and Roohani Sharma and Meirav Zehavi},
journal= {arXiv preprint arXiv:2410.21569},
year = {2026}
}
Comments
Lemma 1 has been phrased as a subroutine that is used recursively by Lemma 2. The earlier version did not take into account that the recursive use of Lemma 1 alone may not be possible without interleaving it with the algorithm of Lemma 2