{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T20:14:32Z","timestamp":1772136872300,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>One of the earliest results in extremal graph theory, Mantel's theorem, states that the maximum number of edges in a triangle-free graph $G$ on $n$ vertices is $\\lfloor n^2\/4 \\rfloor$. We investigate how this extremal bound is affected when $G$ is additionally required to contain a prescribed graph $H$ as a subgraph. We establish general upper and lower bounds for this problem, which are tight in the exponent for random triangle-free graphs and graphs generated by the triangle-free process, when the size of $H$ lies within certain ranges.<\/jats:p>","DOI":"10.37236\/14324","type":"journal-article","created":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T19:43:27Z","timestamp":1772135007000},"source":"Crossref","is-referenced-by-count":0,"title":["Sabotaging Mantel's Theorem"],"prefix":"10.37236","volume":"33","author":[{"given":"Natalie","family":"Behague","sequence":"first","affiliation":[]},{"given":"Debsoumya","family":"Chakraborti","sequence":"additional","affiliation":[]},{"given":"Xizhi","family":"Liu","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2026,2,27]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i1p35\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i1p35\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T19:43:27Z","timestamp":1772135007000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v33i1p35"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,27]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1,9]]}},"URL":"https:\/\/doi.org\/10.37236\/14324","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,27]]},"article-number":"P1.35"}}