Equitable coloring planar graphs with large girth

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 χEq*(G), is the smallest integer m such that G is equitably n  -colorable for all n⩾mn⩾m. We prove that χEq*(G)=χ(G) if G   is a non-bipartite planar graph with girth ⩾26⩾26 and δ(G)⩾2δ(G)⩾2 or G   is a 2-connected outerplanar graph with girth ⩾4⩾4.