On S-packing edge-colorings of cubic graphs

Given a non-decreasing sequence S = (s1, s2, . . . , sk) of positive integers, an Spacking edge-coloring of a graph G is a partition of the edge set of G into k subsets {X1,X2, . . . ,Xk} such that for each 1 ≤ i ≤ k, the distance between two distinct edges e, e′ ∈ Xi is at least si + 1. This paper studies S-packing edgecolorings of cubic graphs. Among other results, we prove that cubic graphs having a 2-factor are (1, 1, 1, 3, 3)-packing edge-colorable, (1, 1, 1, 4, 4, 4, 4, 4)-packing edgecolorable and (1, 1, 2, 2, 2, 2, 2)-packing edge-colorable. We determine sharper results for cubic graphs of bounded oddness and 3-edge-colorable cubic graphs and we propose many open problems.