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arXiv · 1101.4275

3-choosability of planar graphs with (<=4)-cycles far apart

Z. Dvorak
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Abstract

A graph is k-choosable if it can be colored whenever every vertex has a list of at least k available colors. We prove that if cycles of length at most four in a planar graph G are pairwise far apart, then G is 3-choosable. This is analogous to the problem of Havel regarding 3-colorability of planar graphs with triangles far apart.

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Z. Dvorak. 2012-05-25. 3-choosability of planar graphs with (<=4)-cycles far apart. https://arxiv.org/abs/1101.4275

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