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arxiv: 0811.2702 · v1 · submitted 2008-11-17 · 🧮 math.CO

Coloring plane graphs with independent crossings

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keywords planecolorablecrossingsfourgraphsindependentsizealbertson
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We show that every plane graph with maximum face size four whose all faces of size four are vertex-disjoint is cyclically 5-colorable. This answers a question of Albertson whether graphs drawn in the plane with all crossings independent are 5-colorable.

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