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.
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