{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T23:51:21Z","timestamp":1776210681398,"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>Let $\\mu\\left( G\\right) $ be the largest eigenvalue of a graph $G$ and $T_{r}\\left( n\\right) $ be the $r$-partite Tur\u00e1n graph of order $n.$We prove that if $G$ is a graph of order $n$ with $\\mu\\left( G\\right)&gt;\\mu\\left( T_{r}\\left( n\\right) \\right)$, then $G$ contains various large supergraphs of the complete graph of order $r+1,$ e.g., the complete $r$-partite graph with all parts of size $\\log n$ with an edge added to the first part.We also give corresponding stability results.<\/jats:p>","DOI":"10.37236\/122","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:33:10Z","timestamp":1578699190000},"source":"Crossref","is-referenced-by-count":14,"title":["Spectral Saturation: Inverting the Spectral Tur\u00e1n Theorem"],"prefix":"10.37236","volume":"16","author":[{"given":"Vladimir","family":"Nikiforov","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,3,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r33\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r33\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:05:39Z","timestamp":1579298739000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r33"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,3,13]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/122","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,3,13]]},"article-number":"R33"}}