The Equitable Edge-colouring of Outerplanar Graphs

An edge-colouring of a graph \(G\) is \emph{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 \(k \geq 3\).