{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T23:24:24Z","timestamp":1778714664526,"version":"3.51.4"},"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 $F$ be a fixed graph of chromatic number $r+1$. We prove that for all large $n$ the degree sequence of any $F$-free graph of order $n$ is, in a sense, close to being dominated by the degree sequence of some $r$-partite graph. We present two different proofs: one goes via the Regularity Lemma and the other uses a more direct counting argument. Although the latter proof is longer, it gives better estimates and allows $F$ to grow with $n$. As an application of our theorem, we present new results on the generalization of the Tur\u00e1n problem introduced by Caro and Yuster [Electronic J. Combin. 7 (2000)].<\/jats:p>","DOI":"10.37236\/1966","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:08:24Z","timestamp":1578719304000},"source":"Crossref","is-referenced-by-count":2,"title":["Degree Sequences of $F$-Free Graphs"],"prefix":"10.37236","volume":"12","author":[{"given":"Oleg","family":"Pikhurko","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anusch","family":"Taraz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2005,12,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r69\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r69\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:39:28Z","timestamp":1579322368000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v12i1r69"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,12,13]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2005,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1966","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,12,13]]},"article-number":"R69"}}