Maximum Partial List H-Coloring on P_5-free graphs in polynomial time

October 28, 2024 Β· Declared Dead Β· πŸ› arXiv.org

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Authors Daniel Lokshtanov, PaweΕ‚ RzΔ…ΕΌewski, Saket Saurabh, Roohani Sharma, Meirav Zehavi arXiv ID 2410.21569 Category cs.DS: Data Structures & Algorithms Cross-listed cs.CC Citations 3 Venue arXiv.org Last Checked 4 months ago
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 $n^{Ο‰(G)}$-time algorithm for Maximum Partial H-Coloring by Chudnovsky, King, Pilipczuk, RzΔ…ΕΌewski & Spirkl [SIDMA 2021] to polynomial-time algorithm.
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