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

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.

arXiv comment59 pages, 7 figures; revised based on referee remarks

Cited by in corpus (1)

• Note on 3-Choosability of Planar Graphs with Maximum Degree 4