2025/02/24 by Hou, Jingxi, Wang, Tao, Yang, Xiaojing
#05C15 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2502.16962
For a non-decreasing positive integer sequence S = (s1, …, sk), an S-packing edge-coloring of a graph G is a partition of the edge set of G into subsets E1, …, Ek such that for each 1 ≤ i ≤ k, the distance between any two distinct edges e1, e2 ∈ Ei is at least si + 1. Gastineau and Togni conjectured that cubic graphs, except the Petersen and Tietze graphs, admit (1, 1, 1, 3)-packing edge-colorings. In this paper, we prove that every claw-free cubic graph admits such a coloring.