Edge-choosability in line-perfect multigraphs Original Research Article

A multigraph is line-perfect if its line graph is perfect. We prove that if every edge e of a line-perfect multigraph G is given a list containing at least as many colors as there are edges in a largest edge-clique containing e, then G can be edge-colored from its lists. This leads to several characterizations of line-perfect multigraphs in terms of edge-choosability properties. It also proves that these multigraphs satisfy the list-coloring conjecture, which states that if every edge of G is given a list of χ′(G) colors (where χ′ denotes the chromatic index) then G can be edge-colored from its lists. Since bipartite multigraphs are line-perfect, this generalizes Galvinʹs result that the conjecture holds for bipartite multigraphs.