Equitable coloring planar graphs with large girth

Abstract

A proper vertex coloring of a graph G is equitable if the size of color classes differ by at most one. The equitable chromatic threshold of G, denoted by χ Eq * ( G ) , is the smallest integer m such that G is equitably n-colorable for all n ⩾ m . We prove that χ Eq * ( G ) = χ ( G ) if G is a non-bipartite planar graph with girth ⩾ 26 and δ ( G ) ⩾ 2 or G is a 2-connected outerplanar graph with girth ⩾ 4 .