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A Structural Lower Bound for the Ramsey Number of the Petersen Graph — arXiv:2611.09347

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.09347
License (as archived): CC0-1.0
Archived: 2026-11-09T22:43:50.285Z
SHA-256 of the archived text: 31685681bed9713d959da1c3856b64d274e2a0977da68a04f3c0eab58d41ebd2
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How to cite

A Structural Lower Bound for the Ramsey Number of the Petersen Graph — arXiv:2611.09347 — arXiv (en), https://arxiv.org/abs/2611.09347 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_de4efcd16308 (Metraipolis archive dc_de4efcd16308, sha256 31685681bed9713d959da1c3856b64d274e2a0977da68a04f3c0eab58d41ebd2)

BibTeX

@misc{dcde4efcd16308,
  title = {A Structural Lower Bound for the Ramsey Number of the Petersen Graph — arXiv:2611.09347},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.09347},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_de4efcd16308; sha256 31685681bed9713d959da1c3856b64d274e2a0977da68a04f3c0eab58d41ebd2},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.09347. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In this note, we investigate the diagonal Ramsey number of the Petersen graph, denoted by \(R(\mathcal{P}, \mathcal{P})\). To the best of our knowledge, the dynamic survey \textit{Small Ramsey Numbers} (Revision \#18, 2026) records the lower bound as 19, established by Harborth and Krause. We construct a novel 2-coloring on the complete graph \(K_{20}\) that avoids any monochromatic Petersen graph. By defining the blue graph as the complement of the red graph, we utilize a specific join graph structure \(K_{9,9} \vee \overline{K_2}\). We rigorously prove its Petersen-free property, thereby improving the previously documented lower bound to \(R(\mathcal{P}, \mathcal{P}) \ge 21\). Furthermore, we demonstrate the limit of this structural family by showing that the natural extension \(K_{9,9} \vee \overline{K_3}\) contains a Petersen subgraph.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.CO, nuovi lavori del giorno).
Categorie arXiv: Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2611.09347 — 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 2026-11-09T22:36:32.147Z dalla pagina https://arxiv.org/list/math.CO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).