Planar graphs without pairwise adjacent 3-,4-,5-, and 6-cycle are 4-choosable

12/24/2018

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by   Pongpat Sittitrai, et al.

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Xu and Wu proved that if every 5-cycle of a planar graph G is not simultaneously adjacent to 3-cycles and 4-cycles, then G is 4-choosable. In this paper, we improve this result as follows. If G is a planar graph without pairwise adjacent 3-,4-,5-, and 6-cycle, then G is 4-choosable.