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.

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Bonnet et al. (Fri,) studied this question.

synapsesocial.com/papers/68e7b285b6db64358770d434 https://doi.org/https://doi.org/10.48550/arxiv.2402.06338

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1Graphs with girth 9 and without longer odd holes are 3‐colourable2024 · 2 citations
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3Coloring minimal Cayley graphs2024
4Coloring some $(P_6,C_4)$-free graphs with $Δ-1$ colors2024
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1Graphs with girth 9 and without longer odd holes are 3‐colourable2024 · 2 citations
2Graphs with Girth $2\ell+1$ and Without Longer Odd Holes that Contain an Odd $K_4$-Subdivision2024 · 1 citations
3Coloring minimal Cayley graphs2024
4Coloring some $(P_6,C_4)$-free graphs with $Δ-1$ colors2024
5B‐Coloring of Planar Graphs2026