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Maximum Partial List H-Coloring on P_5-free graphs in polynomial time (2410.21569v1)
Published 28 Oct 2024 in cs.DS and cs.CC
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 $n{\omega(G)}$-time algorithm for Maximum Partial H-Coloring by Chudnovsky, King, Pilipczuk, Rz\k{a}.{z}ewski & Spirkl [SIDMA 2021] to polynomial-time algorithm.