{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:10Z","timestamp":1753893850471,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Answering a question of Simonovits and S\u00f3s, Conlon, Fox, and Sudakov proved that for any nonempty graph $H$, and any $\\varepsilon&gt;0$, there exists $\\delta&gt;0$ polynomial in $\\varepsilon$, such that if $G$ is an $n$-vertex graph with the property that every $U\\subseteq V(G)$ contains $p^{e(H)}|U|^{v(H)}\\pm\\delta n^{v(H)}$ labeled copies of $H$, then $G$ is $(p,\\varepsilon)$-quasirandom in the sense that every subset $U\\subseteq G$ contains $\\frac{1}{2}p|U|^{2}\\pm\\varepsilon n^{2}$ edges. They conjectured that $\\delta$ may be taken to be linear in $\\varepsilon$ and proved this in the case that $H$ is a complete graph. We study a labelled version of this quasirandomness property proposed by Reiher and Schacht. Let $H$ be any nonempty graph on $r$ vertices $v_{1},\\ldots,v_{r}$, and $\\varepsilon&gt;0$. We show that there exists $\\delta=\\delta(\\varepsilon)&gt;0$ linear in $\\varepsilon$, such that if $G$ is an $n$-vertex graph with the property that every sequence of $r$ subsets $U_{1},\\ldots,U_{r}\\subseteq V(G)$, the number of copies of $H$ with each $v_{i}$ in $U_{i}$ is $p^{e(H)}\\prod|U_{i}|\\pm\\delta n^{v(H)}$, then $G$ is $(p,\\varepsilon)$-quasirandom.<\/jats:p>","DOI":"10.37236\/7219","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:05:11Z","timestamp":1578668711000},"source":"Crossref","is-referenced-by-count":1,"title":["Linear Dependence Between Hereditary Quasirandomness Conditions"],"prefix":"10.37236","volume":"25","author":[{"given":"Xiaoyu","family":"He","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2018,10,19]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i4p12\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i4p12\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:25:24Z","timestamp":1579235124000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i4p12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,19]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,10,5]]}},"URL":"https:\/\/doi.org\/10.37236\/7219","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,10,19]]},"article-number":"P4.12"}}