Linear algorithm for finding list edge-colorings of series-parallel graphs

Assume that each edge e of a graph G is assigned a list (set) L(e) of colors. Then an edge-coloring of G is called an L-edge-coloring if each edge e of G is colored with a color contained in L(e). It is known that any series-parallel simple graph G has an L-edge-coloring if either (i) \L(e)\ greater than or equal to max {4,d(v),d(w)} for each edge e = vw or (ii) the maximum degree of G is at most three and \L(e)\ greater than or equal to 3 for each edge e, where d(v) and d(w) are the degrees of the ends v and w of e, respectively. In this paper we give a linear-time algorithm for finding such an L-edge-coloring of a series-parallel graph G.