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On the classification of regular graphs with positive Lin-Lu-Yau curvature — arXiv:2609.08903

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.08903
License (as archived): CC0-1.0
Archived: 2026-10-16T14:49:08.380Z
SHA-256 of the archived text: 32e469f27f1960fbd7af2ed579dd15f161888c885999a092e4698c931c3f8f22
Stable URL of this page: https://metraipolis.com/documento/dc_f76a135f8ff0

How to cite

On the classification of regular graphs with positive Lin-Lu-Yau curvature — arXiv:2609.08903 — arXiv (en), https://arxiv.org/abs/2609.08903 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_f76a135f8ff0 (Metraipolis archive dc_f76a135f8ff0, sha256 32e469f27f1960fbd7af2ed579dd15f161888c885999a092e4698c931c3f8f22)

BibTeX

@misc{dcf76a135f8ff0,
  title = {On the classification of regular graphs with positive Lin-Lu-Yau curvature — arXiv:2609.08903},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.08903},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_f76a135f8ff0; sha256 32e469f27f1960fbd7af2ed579dd15f161888c885999a092e4698c931c3f8f22},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.08903. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We prove several new structural and classification results about $d$-regular graphs with positive Lin--Lu--Yau (LLY) curvature. We show that any positively curved $d$-regular graph has diameter at most $2d-2$, which improves the previously best known diameter bound obtained from the Bonnet-Myers-type theorem for positively curved graphs. We further show that every positively curved $d$-regular graph with $d\ge 3$ is $3$-connected. We classify all positively curved $3$-regular graphs, as well as all positively curved regular planar graphs.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-09 in math.CO).
Categorie arXiv: Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2609.08903 — 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 2026-10-16T14:32:29.890Z dalla pagina https://arxiv.org/catchup/math.CO/2026-09-09?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).