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arXiv · 2402.06338

Graphs without a 3-connected subgraph are 4-colorable

Édouard Bonnet·Carl Feghali·Tung Nguyen·Alex Scott·Paul Seymour·Stéphan Thomassé·Nicolas Trotignon
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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.

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Édouard Bonnet, Carl Feghali, Tung Nguyen, Alex Scott, Paul Seymour, Stéphan Thomassé, Nicolas Trotignon. 2024-06-24. Graphs without a 3-connected subgraph are 4-colorable. https://doi.org/10.37236/13181

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