Generalized edge-colorings of weighted graphs.

Let be a graph with a positive integer weight for each vertex . One wishes to assign each edge of a positive integer as a color so that for any vertex and any two edges and incident to . Such an assignment is called an -edge-coloring of , and the maximum integer assigned to edges is called the span of . The -chromatic index of is the minimum span over all -edge-colorings of . In the paper, we present various upper and lower bounds on the -chromatic index, and obtain three efficient algorithms to find an -edge-coloring of a given graph. One of them finds an -edge-coloring with span smaller than twice the -chromatic index. [ABSTRACT FROM AUTHOR]