Characterizing and edge-colouring split-indifference graphs Original Research Article

We describe a simple characterization of graphs which are simultaneouly split and indifference graphs. In the sequel, we present a method for optimally edge colouring a complete graph with an even number ⩾6 of vertices, leading to a simple construction for exhibiting a perfect matching of it, in which all its edges have different colours. Based on the two results, we obtain equations for computing the chromatic index of graphs of the considered class, in linear time. We recall that the chromatic index problem is still unsolved for both classes of split and indifference graphs.