Elsevier

Discrete Mathematics

Volume 309, Issue 8, 28 April 2009, Pages 2424-2431
Discrete Mathematics

On 3-choosable planar graphs of girth at least 4

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Abstract

Let G be a plane graph of girth at least 4. Two cycles of G are intersecting if they have at least one vertex in common. In this paper, we show that if a plane graph G has neither intersecting 4-cycles nor a 5-cycle intersecting with any 4-cycle, then G is 3-choosable, which extends one of Thomassen’s results [C. Thomassen, 3-list-coloring planar graphs of girth 5, J. Combin. Theory Ser. B 64 (1995) 101–107].

Keywords

Colorability
Listing coloring
Planar graphs

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