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 $n^{\omega(G)}$-time algorithm for Maximum Partial H-Coloring by Chudnovsky, King, Pilipczuk, Rz\k{a}\.{z}ewski & Spirkl [SIDMA 2021] to polynomial-time algorithm.

翻译：本文证明了对于任意固定图H，最大部分列表H着色问题在P_5自由图上均存在多项式时间解法。特别地，这意味着最大k可着色子图问题在P_5自由图上也是多项式时间可解的。该结论回答了Agrawal、Lima、Lokshtanov、Saurabh与Sharma在[SODA 2024]中提出的公开问题。同时，本研究将Chudnovsky、King、Pilipczuk、Rzążewski与Spirkl在[SIDMA 2021]中提出的最大部分H着色问题的$n^{\omega(G)}$时间复杂度算法改进为多项式时间算法。