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 \(k \geq 3\).
Citation
Jian-Liang Wu. The Equitable Edge-colouring of Outerplanar Graphs[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 036. 247-253. .