The circular chromatic index Original Research Article

A (k,d)-edge coloring (k,d∈N, k⩾2d) of a graph G is an assignment c of colors {0,1,…,k−1} to the edges of G such that d⩽|c(ei)−c(ej)|⩽k−d whenever two edges ei and ej are adjacent. The circular chromatic index χc′(G) is defined by χc′(G)=inf{k/d:G has a (k,d)-edge coloring}. We prove several properties of χc′(G) and determine exact values for some classes of graphs.