A simple and fast heuristic algorithm for edge-coloring of graphs

Abstract

A simple but empirically efficient heuristic algorithm for the edge-coloring of graphs is presented. Its basic idea is the displacement of "conflicts" (repeated colors in the edges incident to a vertex) along paths of adjacent vertices whose incident edges are recolored by swapping alternating colors (that is, doing a Kempe interchange). The results of performance tests on random cubic and $\Delta$-regular graphs are presented, and a full implementation of the algorithm is given to facilitate its use and the reproducibility of results.