The IsEdgeColorable(G,k) function returns true if the graph G is k-edge colorable and false otherwise.  That is, if the edges of G can be colored with k colors such that no two incident edges have the same color.

If an optional argument d is specified, then IsEdgeColorable(G,k,d) returns true if the graph G is (k,d)-edge colorable, and false otherwise. That is, it returns true if the edges of G can be colored with k colors such that two edges with any given color are at least distance d apart.  When d is not specified it is assumed to be 1.

If a name col is specified, then this name is assigned the list of colors of an optimal proper coloring of edges of G, if it exists. The algorithm uses a backtracking technique.