English

Obstructions for three-coloring and list three-coloring $H$-free graphs

Combinatorics 2018-02-08 v4 Discrete Mathematics

Abstract

A graph is HH-free if it has no induced subgraph isomorphic to HH. We characterize all graphs HH for which there are only finitely many minimal non-three-colorable HH-free graphs. Such a characterization was previously known only in the case when HH is connected. This solves a problem posed by Golovach et al. As a second result, we characterize all graphs HH for which there are only finitely many HH-free minimal obstructions for list 3-colorability.

Keywords

Cite

@article{arxiv.1703.05684,
  title  = {Obstructions for three-coloring and list three-coloring $H$-free graphs},
  author = {Maria Chudnovsky and Jan Goedgebeur and Oliver Schaudt and Mingxian Zhong},
  journal= {arXiv preprint arXiv:1703.05684},
  year   = {2018}
}

Comments

40 pages

R2 v1 2026-06-22T18:47:53.332Z