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Linear hereditary quasirandomness — arXiv:2610.39317

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.39317
License (as archived): CC0-1.0
Archived: 2026-11-01T02:37:52.829Z
SHA-256 of the archived text: 4990c73f2416ed27763ebbefbe955777d307011bab2a7b219b8bab91cdecd4b7
Stable URL of this page: https://metraipolis.com/documento/dc_101fb76d366e

How to cite

Linear hereditary quasirandomness — arXiv:2610.39317 — arXiv (en), https://arxiv.org/abs/2610.39317 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_101fb76d366e (Metraipolis archive dc_101fb76d366e, sha256 4990c73f2416ed27763ebbefbe955777d307011bab2a7b219b8bab91cdecd4b7)

BibTeX

@misc{dc101fb76d366e,
  title = {Linear hereditary quasirandomness — arXiv:2610.39317},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.39317},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_101fb76d366e; sha256 4990c73f2416ed27763ebbefbe955777d307011bab2a7b219b8bab91cdecd4b7},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.39317. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Conlon, Fox and Sudakov (\emph{Math. Proc. Cambridge Philos. Soc.} \textbf{164} (2018), 385--399) conjectured that hereditary subgraph counts force quasirandomness with linear dependence on the counting error. We prove this for every graph containing an edge. Let \(H\) have \(r\) vertices and \(m\ge1\) edges, and fix \(p\in(0,1)\). If every subset \(S\) of an \(n\)-vertex graph \(G\) contains \(p^m|S|^r\pm\delta n^r\) labelled injective copies of \(H\), then \(\lvert e_G(A,B)-p|A||B|\rvert\le C_{H,p}\delta n^2\) for all \(A,B\subseteq V(G)\), where \(e_G(A,B)\) counts ordered adjacent pairs. The proof extracts averaged rooted counts and represents each nonlinear term by a linear map in one selected edge factor. Composing two such maps gives an edge substitution with a superlinear cut-norm bound. A separate star expansion gives stronger local estimates for triangle-free graphs. The linear order is best possible even when \(2e(G)/n^2=p+O(n^{-2})\).

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/2610.39317 — 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 2026-11-01T02:15:28.269Z dalla pagina https://arxiv.org/list/math.CO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).