Metraipolis › archive › dc_6cecf809fb8d

Supersaturation of induced even cycles in locally sparse graphs — arXiv:2608.04985

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.04985
License (as archived): CC0-1.0
Archived: 2026-10-31T11:46:05.078Z
SHA-256 of the archived text: 3bd3c08cd3f9df4d172f8491948615df23b075bbd4d00a165f3e58fac5a67288
Stable URL of this page: https://metraipolis.com/documento/dc_6cecf809fb8d

How to cite

Supersaturation of induced even cycles in locally sparse graphs — arXiv:2608.04985 — arXiv (en), https://arxiv.org/abs/2608.04985 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_6cecf809fb8d (Metraipolis archive dc_6cecf809fb8d, sha256 3bd3c08cd3f9df4d172f8491948615df23b075bbd4d00a165f3e58fac5a67288)

BibTeX

@misc{dc6cecf809fb8d,
  title = {Supersaturation of induced even cycles in locally sparse graphs — arXiv:2608.04985},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.04985},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_6cecf809fb8d; sha256 3bd3c08cd3f9df4d172f8491948615df23b075bbd4d00a165f3e58fac5a67288},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.04985. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

A graph $\Gamma$ is $(c,t)$-sparse for $c > 0$ and $t \ge 1$ if for every pair of vertex subsets $A, B \subseteq V(\Gamma)$ with $|A|, |B| \ge t$, the number of edges $e(A,B)$ between them satisfies $ e(A,B) \le (1 - c)|A||B|$. In this paper, we prove that for every integer $\ell\ge2$, there are $\varepsilon > 0, C, C' > 0$ such that if an $n$-vertex graph $\Gamma$ is $(1-\varepsilon,t)$-sparse for some $t$, and has at least $Ct^{1-1/\ell}n^{1+1/\ell}$ edges, then $\Gamma$ contains at least $C'n^2t^{2\ell-2}$ induced copies of $C_{2\ell}$. This partially resolves a problem of Ding, Gao, Liu, Luan, and Sun.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-06 in math.CO).
Categorie arXiv: Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2608.04985 — 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 2026-10-31T11:35:10.109Z dalla pagina https://arxiv.org/catchup/math.CO/2026-08-06?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).