English

Graphs without a 3-connected subgraph are 4-colorable

Combinatorics 2025-11-04 v2 Discrete Mathematics

Abstract

In 1972, Mader showed that every graph without a 3-connected subgraph is 4-degenerate and thus 5-colorable}. We show that the number 5 of colors can be replaced by 4, which is best possible.

Keywords

Cite

@article{arxiv.2402.06338,
  title  = {Graphs without a 3-connected subgraph are 4-colorable},
  author = {Édouard Bonnet and Carl Feghali and Tung Nguyen and Alex Scott and Paul Seymour and Stéphan Thomassé and Nicolas Trotignon},
  journal= {arXiv preprint arXiv:2402.06338},
  year   = {2025}
}

Comments

13 pages

R2 v1 2026-06-28T14:43:56.814Z