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On $(1,2^4)$ and $(1,2^5)$-packing edge-coloring of sparse subcubic graphs — arXiv:2608.29163

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.29163
License (as archived): CC0-1.0
Archived: 2026-10-17T09:30:55.881Z
SHA-256 of the archived text: 23f44de904f5949d820adcee6e010ed98474c99e4ade47cff96415e6236cad1b
Stable URL of this page: https://metraipolis.com/documento/dc_b65dff9720ff

How to cite

On $(1,2^4)$ and $(1,2^5)$-packing edge-coloring of sparse subcubic graphs — arXiv:2608.29163 — arXiv (en), https://arxiv.org/abs/2608.29163 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_b65dff9720ff (Metraipolis archive dc_b65dff9720ff, sha256 23f44de904f5949d820adcee6e010ed98474c99e4ade47cff96415e6236cad1b)

BibTeX

@misc{dcb65dff9720ff,
  title = {On $(1,2^4)$ and $(1,2^5)$-packing edge-coloring of sparse subcubic graphs — arXiv:2608.29163},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.29163},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_b65dff9720ff; sha256 23f44de904f5949d820adcee6e010ed98474c99e4ade47cff96415e6236cad1b},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.29163. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

A $(1^j,2^k)$-packing edge-coloring of a graph $G$ is a partition of the edge set $E(G)$ into $j$ matchings and $k$ induced matchings. Hocquard, Lajou, and Lu\v zar found a subcubic planar graph of girth $3$ that has no $(1,2^5)$-packing edge-coloring and also conjectured that every subcubic planar graph has a $(1,2^6)$-packing edge-coloring. We also notice that for every fixed positive integer $k$ there exists a subcubic planar graph with girth $k$ that is not $(1,2^3)$-packing edge-colorable. It is natural to consider what is the minimum positive integer $k_1$ such that every subcubic planar graph with girth at least $k_1$ is $(1,2^5)$-packing edge-colorable. Furthermore, we also consider what is the minimum positive integer $k_2$ such that every subcubic planar graph with girth at least $k_2$ is $(1,2^4)$-packing edge-colorable. In this paper, we show both $k_1$ and $k_2$ are finite, and in fact $5 \le k_1 \le 12$ and $6 \le k_2 \le 16$.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-01 in math.CO).
Categorie arXiv: Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2608.29163 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-17T09:02:28.816Z dalla pagina https://arxiv.org/catchup/math.CO/2026-09-01?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).