On S-packing edge-colorings of cubic graphs

Nicolas Gastineau (1, 2) , Olivier Togni (3)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
2 Le2i - Equipe combinatoire
3 Le2i - Laboratoire Electronique, Informatique et Image [UMR6306]

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 ′ ∈ X i is at least s i + 1. 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.

Domaines: Mathématique discrète [cs.DM]

Nicolas Gastineau, Olivier Togni. On S-packing edge-colorings of cubic graphs. 2017. ⟨hal-01651260⟩