Equitable colorings of outerplanar graphs

Abstract

A proper vertex coloring of a graph is equitable if the sizes of color classes differ by at most 1. In this note, we prove the conjecture of Yap and Zhang that every outerplanar graph with maximum degree at most Δ admits an equitable k-coloring for every k⩾1+ Δ/2. This restriction on k cannot be weakened.