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arXiv · 2011.06173

On 3-Coloring of $(2P_4,C_5)$-Free Graphs

Vít Jelínek·Tereza Klimošová·Tomáš Masařík·Jana Novotná·Aneta Pokorná
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Abstract

The 3-coloring of hereditary graph classes has been a deeply-researched problem in the last decade. A hereditary graph class is characterized by a (possibly infinite) list of minimal forbidden induced subgraphs $H_1,H_2,\ldots$; the graphs in the class are called $(H_1,H_2,\ldots)$-free. The complexity of 3-coloring is far from being understood, even for classes defined by a few small forbidden induced subgraphs. For $H$-free graphs, the complexity is settled for any $H$ on up to seven vertices. There are only two unsolved cases on eight vertices, namely $2P_4$ and $P_8$. For $P_8$-free graphs, some partial results are known, but to the best of our knowledge, $2P_4$-free graphs have not been explored yet. In this paper, we show that the 3-coloring problem is polynomial-time solvable on $(2P_4,C_5)$-free graphs.

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Vít Jelínek, Tereza Klimošová, Tomáš Masařík, Jana Novotná, Aneta Pokorná. 2020-11-12. On 3-Coloring of $(2P_4,C_5)$-Free Graphs. https://doi.org/10.1007/s00453-022-00937-9%2010.1007%2F978-3-030-86838-3_30

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