{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,25]],"date-time":"2026-07-25T02:33:45Z","timestamp":1784946825792,"version":"3.55.0"},"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>Consider a graph $G$ on $n$ vertices with $\\alpha \\binom{n}{2}$ edges which does not contain an induced $K_{2, t}$ ($t \\geqslant 2$). How large must $\\alpha$ be to ensure that $G$ contains, say, a large clique or some fixed subgraph $H$? We give results for two regimes: for $\\alpha$ bounded away from zero and for $\\alpha = o(1)$.\r\nOur results for $\\alpha = o(1)$ are strongly related to the Induced Tur\u00e1n numbers which were recently introduced by Loh, Tait, Timmons and Zhou. For $\\alpha$ bounded away from zero, our results can be seen as a generalisation of a result of Gy\u00e1rf\u00e1s, Hubenko and Solymosi and more recently Holmsen (whose argument inspired ours).<\/jats:p>","DOI":"10.37236\/9223","type":"journal-article","created":{"date-parts":[[2021,2,11]],"date-time":"2021-02-11T10:12:08Z","timestamp":1613038328000},"source":"Crossref","is-referenced-by-count":4,"title":["Graphs with no Induced $K_{2, t}$"],"prefix":"10.37236","volume":"28","author":[{"given":"Freddie","family":"Illingworth","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2021,1,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i1p19\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i1p19\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,11]],"date-time":"2021-02-11T10:12:09Z","timestamp":1613038329000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v28i1p19"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,29]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,1,14]]}},"URL":"https:\/\/doi.org\/10.37236\/9223","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,29]]},"article-number":"P1.19"}}