3-choosability of planar graphs with (<=4)-cycles far apart
Combinatorics
2012-05-28 v2 Discrete Mathematics
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.
Cite
@article{arxiv.1101.4275,
title = {3-choosability of planar graphs with (<=4)-cycles far apart},
author = {Z. Dvorak},
journal= {arXiv preprint arXiv:1101.4275},
year = {2012}
}
Comments
59 pages, 7 figures; revised based on referee remarks