English

List-three-coloring graphs with no induced $P_6+rP_3$

Combinatorics 2018-07-03 v2

Abstract

For an integer rr, the graph P6+rP3P_6+rP_3 has r+1r+1 components, one of which is a path on 66 vertices, and each of the others is a path on 33 vertices. In this paper we provide a polynomial-time algorithm to test if a graph with no induced subgraph isomorphic to P6+rP3P_6+rP_3 is three-colorable. We also solve the list version of this problem, where each vertex is assigned a list of possible colors, which is a subset of {1,2,3}\{1,2,3\}.

Keywords

Cite

@article{arxiv.1806.11196,
  title  = {List-three-coloring graphs with no induced $P_6+rP_3$},
  author = {Maria Chudnovsky and Shenwei Huang and Sophie Spirkl and Mingxian Zhong},
  journal= {arXiv preprint arXiv:1806.11196},
  year   = {2018}
}