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)| 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)| 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.

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). In this paper, we prove that any series-parallel simple graph G has an L-edge-coloring if |L(e)| max{3,d(v),d(w)} for each edge e = vw, where d(v) and d(w) are the degrees of the ends v and w of e, respectively. Our proof yields a linear algorithm for finding an L-edge-coloring of series-parallel graphs.