Planar graphs without pairwise adjacent 3-,4-,5-, and 6-cycle are 4-choosable (1812.10473v2)

Abstract: 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.