Graphs without a 3-connected subgraph are 4-colorable
<|reference_start|>Graphs without a 3-connected subgraph are 4-colorable: 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.<|reference_end|>
@article{bonnet2024graphs,
    title={Graphs without a 3-connected subgraph are 4-colorable},
    author={'Edouard Bonnet and Carl Feghali and Tung Nguyen and Alex Scott and
  Paul Seymour and St'ephan Thomass'e and Nicolas Trotignon},
    journal={arXiv preprint arXiv:2402.06338},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.06338},
    primaryClass={math.CO cs.DM}
}