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On S-packing edge-colorings of cubic graphs

Gastineau, Nicolas; Togni, Olivier (2019), On S-packing edge-colorings of cubic graphs, Discrete Applied Mathematics, 259, p. 63-75. 10.1016/j.dam.2018.12.035

Type
Article accepté pour publication ou publié
External document link
https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01651260
Date
2019
Journal name
Discrete Applied Mathematics
Volume
259
Publisher
Elsevier
Pages
63-75
Publication identifier
Metadata
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Author(s)
Gastineau, Nicolas
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Togni, Olivier cc
Abstract (EN)
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.
Subjects / Keywords
Cubic graph; Packing chromatic index; S-packing chromatic index; Snark; d,-distance coloring