{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:54Z","timestamp":1753893834786,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Graphs with large minimum degree containing no copy of a clique on $r$ vertices ($K_r$) must contain relatively large independent sets. A classical result of Andr\u00e1sfai, Erd\u0151s, and S\u00f3s implies that $K_r$-free graphs $G$ with degree larger than $((3r-7)\/(3r-4))|V(G)|$ must be $(r-1)$-partite. An obvious consequence of this result is that the same degree threshold implies an independent set of order $(1\/(r-1))|V(G)|$.\u00a0The following paper provides improved bounds on the minimum degree which would imply the same conclusion. This problem was first considered by Brandt, and we provide improvements over these initial results for $r &gt; 5$.<\/jats:p>","DOI":"10.37236\/3881","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:04:25Z","timestamp":1578704665000},"source":"Crossref","is-referenced-by-count":5,"title":["A Note on Independent Sets in Graphs with Large Minimum Degree and Small Cliques"],"prefix":"10.37236","volume":"21","author":[{"given":"Jeremy","family":"Lyle","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2014,5,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i2p38\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i2p38\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:59:04Z","timestamp":1579258744000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v21i2p38"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,5,22]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2014,3,31]]}},"URL":"https:\/\/doi.org\/10.37236\/3881","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2014,5,22]]},"article-number":"P2.38"}}