Packing edge-colorings of subcubic outerplanar graphs
Sijin Li, Yifan Li, Xujun Liu

TL;DR
This paper proves that all subcubic outerplanar graphs can be edge-colored with specific packing constraints, confirming a conjecture for this class and establishing optimal bounds for such colorings.
Contribution
It confirms a conjecture on packing edge-colorings of subcubic outerplanar graphs and determines the best possible bounds for these colorings.
Findings
Every subcubic outerplanar graph has a (1,2^5)-coloring.
Every subcubic outerplanar graph has a (1^2,2^3)-coloring.
Bounds for k_1 and k_2 in extended colorability are established.
Abstract
For a sequence of non-decreasing positive integers, an -packing edge-coloring (S-coloring) of a graph is a partition of into such that the distance between each pair of distinct edges , , is at least . In particular, a -coloring is a partition of into matchings and induced matchings, and it can be viewed as intermediate colorings between proper and strong edge-colorings. Hocquard, Lajou, and Lu\v{z}ar conjectured that every subcubic planar graph has a -coloring and a -coloring. In this paper, we confirm the conjecture of Hocquard, Lajou, and Lu\v{z}ar for subcubic outerplanar graphs by showing every subcubic outerplanar graph has a -coloring and a -coloring. Our results are best possible since we found…
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Taxonomy
Topicsgraph theory and CDMA systems · Advanced Graph Theory Research · Graph Labeling and Dimension Problems
