{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T15:19:10Z","timestamp":1777562350338,"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>A conjecture of Loebl, also known as the $(n\/2 - n\/2 - n\/2)$ Conjecture, states that if $G$ is an $n$-vertex graph in which at least $n\/2$ of the vertices have degree at least $n\/2$, then $G$ contains all trees with at most $n\/2$ edges as subgraphs. Applying the Regularity Lemma, Ajtai, Koml\u00f3s and Szemer\u00e9di proved an approximate version of this conjecture. We prove it exactly for sufficiently large $n$. This immediately gives a tight upper bound for the Ramsey number of trees, and partially confirms a conjecture of Burr and Erd\u0151s.<\/jats:p>","DOI":"10.37236\/514","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:56:41Z","timestamp":1578715001000},"source":"Crossref","is-referenced-by-count":13,"title":["Proof of the $(n\/2-n\/2-n\/2)$ Conjecture for Large $n$"],"prefix":"10.37236","volume":"18","author":[{"given":"Yi","family":"Zhao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,2,4]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p27\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p27\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:17:28Z","timestamp":1579303048000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p27"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,2,4]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/514","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,2,4]]},"article-number":"P27"}}