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Obstructions for three-coloring graphs without induced paths on six vertices

Combinatorics 2018-02-20 v2 Discrete Mathematics
Authors: Maria Chudnovsky , Jan Goedgebeur , Oliver Schaudt , Mingxian Zhong
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Abstract

We prove that there are 24 4-critical P6P_6-free graphs, and give the complete list. We remark that, if HH is connected and not a subgraph of P6P_6, there are infinitely many 4-critical HH-free graphs. Our result answers questions of Golovach et al. and Seymour.

Keywords

graph coloring graph theory

Cite

@article{arxiv.1504.06979,
  title  = {Obstructions for three-coloring graphs without induced paths on six vertices},
  author = {Maria Chudnovsky and Jan Goedgebeur and Oliver Schaudt and Mingxian Zhong},
  journal= {arXiv preprint arXiv:1504.06979},
  year   = {2018}
}

Comments

31 pages

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