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An explicit bound on the extremal function for complete graph minors — arXiv:2610.41060

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.41060
License (as archived): CC0-1.0
Archived: 2026-11-03T08:17:57.340Z
SHA-256 of the archived text: e74a9995baf2d0a33b5bbb884234a3826abe82c8464eb08682932d12396e0d84
Stable URL of this page: https://metraipolis.com/documento/dc_4ba2522bb2fa

How to cite

An explicit bound on the extremal function for complete graph minors — arXiv:2610.41060 — arXiv (en), https://arxiv.org/abs/2610.41060 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_4ba2522bb2fa (Metraipolis archive dc_4ba2522bb2fa, sha256 e74a9995baf2d0a33b5bbb884234a3826abe82c8464eb08682932d12396e0d84)

BibTeX

@misc{dc4ba2522bb2fa,
  title = {An explicit bound on the extremal function for complete graph minors — arXiv:2610.41060},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.41060},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_4ba2522bb2fa; sha256 e74a9995baf2d0a33b5bbb884234a3826abe82c8464eb08682932d12396e0d84},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.41060. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Kostochka and Thomason independently proved that every graph with density at least $\beta\,t\sqrt{\log t}$ has a $K_t$ minor, for some constant $\beta$. Thomason later proved that the least such density is $(0.319\ldots+o(1))\,t\sqrt{\log t}$. However, the $o(1)$ term in this formula is not explicit, so the formula gives no bound for any specific value of $t$. The goal of this paper is a bound of the form $\beta\,t\sqrt{\log t}$ that holds for every $t$, with $\beta$ small. We prove that, for every integer $t\geqslant2$, every graph with density at least $4.5\,t\sqrt{\log t}$ has a $K_t$ minor.

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/2610.41060 — 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 2026-11-03T08:05:23.767Z dalla pagina https://arxiv.org/list/math.CO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).