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.

MSC codes

  1. 05C15
  2. 05C10

Keywords

  1. choosability
  2. graph coloring
  3. crossing number

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References

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Published In

cover image SIAM Journal on Discrete Mathematics
SIAM Journal on Discrete Mathematics
Pages: 1746 - 1753
ISSN (online): 1095-7146

History

Submitted: 10 March 2011
Accepted: 20 September 2011
Published online: 8 December 2011

MSC codes

  1. 05C15
  2. 05C10

Keywords

  1. choosability
  2. graph coloring
  3. crossing number

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