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). In this paper, we prove that any series-parallel simple graph G has an L-edge-coloring if \L(e)\ greater than or equal to max {3,d(upsilon),d(omega)} for each edge e = upsilonw, where d(upsilon) and d(omega) are the degrees of the ends upsilon and omega of e, respectively. Our proof yields a linear algorithm for finding an L-edge-coloring of series-parallel graphs.