List star edge-coloring of [formula omitted]-degenerate graphs and [formula omitted]-minor free graphs

Abstract

A star edge-coloring of a graph G is a proper edge-coloring without 2-colored paths and cycles of length 4. For a graph G, let the list star chromatic index of G be the minimum k such that for any k-uniform list assignment L for the set of edges, G has a star edge-coloring from L. In this paper we prove that the list star chromatic index of every k-degenerate graph G with maximum degree Δ is at most (3k−2)Δ−k2+2. For K4-minor free graphs (k=2), we decrease this bound to 3Δ−3, Δ≥3. We do not use the discharging method but rather we use the fundamental structural properties of k-degenerate graphs and K4-minor free graphs.