On S-packing edge-colorings of cubic graphs
Discrete Mathematics
2017-11-30 v1 Combinatorics
Abstract
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.
Keywords
Cite
@article{arxiv.1711.10906,
title = {On S-packing edge-colorings of cubic graphs},
author = {Nicolas Gastineau and Olivier Togni},
journal= {arXiv preprint arXiv:1711.10906},
year = {2017}
}