Rich-neighbor 5-edge-colorings of subcubic graphs whose 3-vertices induce a matching

@misc{kong2026richneighbor,
  title = {{Rich-neighbor 5-edge-colorings of subcubic graphs whose 3-vertices induce a matching}},
  author = {Jiangxu Kong and Zhuming Lin and Yan Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.21868},
  eprint = {2610.21868},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.21868},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Rich-neighbor 5-edge-colorings of subcubic graphs whose 3-vertices induce a matching
AU  - Jiangxu Kong
AU  - Zhuming Lin
AU  - Yan Wang
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.21868
UR  - https://arxiv.org/abs/2610.21868
AB  - Let φ be a proper edge-coloring of a graph G. An edge is called rich if all edges adjacent to it receive pairwise distinct colors. The coloring φ is a rich-neighbor edge-coloring if every non-isolated edge is adjacent to a rich edge. Petruševski and Škrekovski introduced this notion as a relaxation of strong edge-coloring and conjectured that every connected subcubic graph other than K_4 admits a rich-neighbor $5$-edge-coloring. We establish the conjectured bound for every subcubic graph G satisfying Δ(G[V_3])≤ 1, where V_3 is the set of vertices of degree $3$ in G. Equivalently, the $3$-vertices of G induce a matching together with isolated vertices. This extends the result of Chen, Tan and Zhou for subcubic graphs with no adjacent $3$-vertices.
ER  -