Publication at Faculty of Mathematics and Physics |
2014
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.