Equitable coloring and equitable choosability of planar graphs without 5- and 7-cycles - Tuan Norhafizah binti Tuan Zakaria (Bulletin of the Malaysian Mathematical Sciences Society , Malaysian Mathematical Sciences Society, Universiti Sains Malaysia, Springer, 2012)
A graph G is equitably k-choosable if for any k-uniform list assignment L, G is L-colorable and each color appears on at most djV(G)j=ke vertices. A graph G is equitable kcolorable if G has a proper vertex coloring with k colors such that the size of the color classes differ by at most 1. In this paper, we prove that if G is a planar graph without 5- and 7-cycles, then G is equitably k-choosable and equitably k-colorable where k maxfD(G)