{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:01Z","timestamp":1753893841858,"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>We determine the maximum number of edges of an $n$-vertex graph $G$ with\u00a0the property that none of its $r$-cliques intersects a fixed set\u00a0$M\\subset V(G)$.\u00a0 For $(r-1)|M|\\ge n$, the $(r-1)$-partite Tur\u00e1n graph\u00a0turns out to be the unique extremal graph. For $(r-1)|M|&lt;n$, there is a\u00a0whole family of extremal graphs, which we describe explicitly. In\u00a0addition we provide corresponding stability results.<\/jats:p>","DOI":"10.37236\/4194","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:54:25Z","timestamp":1578704065000},"source":"Crossref","is-referenced-by-count":1,"title":["An Extension of Tur\u00e1n's Theorem, Uniqueness and Stability"],"prefix":"10.37236","volume":"21","author":[{"given":"Peter","family":"Allen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Julia","family":"B\u00f6ttcher","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jan","family":"Hladk\u00fd","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Diana","family":"Piguet","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2014,10,2]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i4p5\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i4p5\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:43:54Z","timestamp":1579257834000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v21i4p5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,10,2]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2014,10,2]]}},"URL":"https:\/\/doi.org\/10.37236\/4194","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2014,10,2]]},"article-number":"P4.5"}}