{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T00:54:13Z","timestamp":1761008053918,"version":"build-2065373602"},"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>Zykov and Erd\u0151s showed independently that for $2\\le s\\le r$, the maximum number of copies of $K_s$ among all $K_r$-free $n$-vertex graphs is achieved uniquely on the complete balanced $r$-partite $n$-vertex graph (Tur\u00e1n graph $T_{n,r}$). When $s=2$, it is the classical theorem of Tur\u00e1n. Nikiforov proved a spectral version of Tur\u00e1n's Theorem. In this paper, we give a spectral version of the theorem by Zykov and Erd\u0151s. Our result is a generalization of Nikiforov's Theorem and a theorem of Liu and Bu.<\/jats:p>","DOI":"10.37236\/14119","type":"journal-article","created":{"date-parts":[[2025,10,20]],"date-time":"2025-10-20T22:53:38Z","timestamp":1761000818000},"source":"Crossref","is-referenced-by-count":0,"title":["A Spectral Version of the Theorem of Zykov and Erd\u0151s"],"prefix":"10.37236","volume":"32","author":[{"given":"Loujun","family":"Yu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuejian","family":"Peng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2025,10,17]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i4p15\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i4p15\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,20]],"date-time":"2025-10-20T22:53:38Z","timestamp":1761000818000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v32i4p15"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,17]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,10,3]]}},"URL":"https:\/\/doi.org\/10.37236\/14119","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,17]]},"article-number":"P4.15"}}