On 3Coloring of $(2P_4,C_5)$Free Graphs
Abstract
The 3coloring of hereditary graph classes has been a deeplyresearched 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 3coloring 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 3coloring problem is polynomialtime solvable on $(2P_4,C_5)$free graphs.
 Publication:

arXiv eprints
 Pub Date:
 November 2020
 DOI:
 10.48550/arXiv.2011.06173
 arXiv:
 arXiv:2011.06173
 Bibcode:
 2020arXiv201106173J
 Keywords:

 Computer Science  Data Structures and Algorithms;
 Computer Science  Discrete Mathematics;
 Mathematics  Combinatorics;
 05C15;
 05C85
 EPrint:
 18 pages, 13 figures. Accepted to International Workshop on GraphTheoretic Concepts in Computer Science (WG) 2021