On S-packing edge-colorings of cubic graphs

Given a non-decreasing sequence S = (s(1), s(2), ... , s(k)) of positive integers, an S-packing edge-coloring of a graph G is a partition of the edge set of G into k subsets {X-1, X-2, ... , X-k} such that for each 1 <= i <= k, the distance between two distinct edges e, e' is an element of X-i is at least s(i) + 1 (where the edge-distance in G is defined as the vertex-distance in the line-graph of G). This paper studies S-packing edge-colorings 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 edge-colorable 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. (C) 2019 Elsevier B.V. All rights reserved.