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

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 $H_1,H_2,\dots$; the graphs in the class are called $(H_1,H_2,\dots )$-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.

18 pages, 13 figures. Accepted to International Workshop on Graph-Theoretic Concepts in Computer Science (WG) 2021

References in corpus (1)

• Better 3-coloring algorithms: excluding a triangle and a seven vertex path