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Coloring graphs with crossings

Bogdan Oporowski·David Zhao
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Abstract

We generalize the Five Color Theorem by showing that it extends to graphs with two crossings. Furthermore, we show that if a graph has three crossings, but does not contain K_6 as a subgraph, then it is also 5-colorable. We also consider the question of whether the result can be extended to graphs with more crossings.

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Bogdan Oporowski, David Zhao. 2005-01-25. Coloring graphs with crossings. https://arxiv.org/abs/math/0501427

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