Choosability of planar graphs of girth 5

Details Choosability of planar graphs of girth 5 Choosability of planar graphs of girth 5

2011-09-14

arxiv.org/abs/1109.2976v1

Mathematics

Combinatorics

44 pages, 6 figures

Scientific paper

Thomassen proved that any plane graph of girth 5 is list-colorable from any list assignment such that all vertices have lists of size two or three and the vertices with list of size two are all incident with the outer face and form an independent set. We present a strengthening of this result, relaxing the constraint on the vertices with list of size two. This result is used to bound the size of the 3-list-coloring critical plane graphs with one precolored face.

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