List strong edge coloring of planar graphs with maximum degree 4

Abstract A strong-edge-coloring of a graph is a proper edge coloring in which every color class is an induced matching. The strong chromatic index of G , denoted by χ s ′ ( G ) , is the minimum number of colors to construct such a coloring. In an analogous way, we can define the list version of strong chromatic index. In this paper we prove that if G is a planar graph with maximum degree at most four , then the list strong chromatic index is at most 19.