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

Authors:
Zdenk Dvořák
Affiliations:
-
Venue:
Journal of Combinatorial Theory Series B
Year:
2014

Citing 6
Cited 0

List colourings of planar graphs

Discrete Mathematics
Every planar graph is 5-choosable

Journal of Combinatorial Theory Series B
Algorithmic complexity of list colorings

Discrete Applied Mathematics
3-list-coloring planar graphs of girth 5

Journal of Combinatorial Theory Series B
A not 3-choosable planar graph without 3-cycles

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The chromatic number of a graph of girth 5 on a fixed surface

Journal of Combinatorial Theory Series B

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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.