The Equitable Edge-colouring of Outerplanar Graphs

Abstract

An edge-colouring of a graph $G$ is $equitable$ if, for each vertex $v$ of $G$, the number of edges of any one colour incident with $v$ differs from the number of edges of any other colour incident with $v$ by at most one. In the paper, we prove that any outerplanar graph has an equitable edge-colouring with $k$ colours for any integer $k\ge 3$.