Equitable and equitable list colorings of graphs

A proper k-vertex coloring of a graph is an equitable k-coloring if the sizes of the color classes differ by at most 1. 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 vertices. We prove in this paper that outerplane graphs are equitably k-choosable whenever k≥Δ, where Δ is the maximum degree. Moreover, we discuss equitable colorings of some d-degenerate graphs.