List Equitable Coloring of Planar Graphs without 4- and 6-Cycles when (G) =5

A graph G is k list equitably colorable, if for any given k-uniform list assignment L, G is L-colorable and each color appears on at most |V (G) |k vertices. In 2009, Li and Bu obtained that for planar graph G, if (G) 6 and without 4- and 6-cycles, then G is (G) list equitably colorable. In order to further prove the conjecture of list equitable coloring, in this paper, we focus on planar graph with (G) =5, and prove that if G is a planar graph without 4- and 6-cycles, then G is (G) list equitably colorable.