Graphs with Two Crossings Are 5-Choosable

Authors:
Zdeněk Dvořák;Bernard Lidický;Riste Škrekovski
Affiliations:
rakdver@kam.mff.cuni.cz and bernard@kam.mff.cuni. cz;-;skrekovski@gmail.com
Venue:
SIAM Journal on Discrete Mathematics
Year:
2011

Citing 6
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Abstract

A graph $G$ is $k$-choosable if $G$ can be properly colored whenever every vertex has a list of at least $k$ available colors. Thomassen's theorem states that every planar graph is 5-choosable. We extend the result by showing that every graph with at most two crossings is 5-choosable.