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

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

2011-01-22

arxiv.org/abs/1101.4275v1

Mathematics

Combinatorics

54 pages, 7 figures

Scientific paper

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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