{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:28Z","timestamp":1753893868504,"version":"3.41.2"},"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>Erd\u0151s and S\u00f3s\u00a0conjectured that every graph $G$\u00a0of average degree greater than $k-1$ contains every tree of size $k$. Several results based upon the number of vertices in $G$ have been proved including the special cases where $G$ has exactly $k+1$ vertices (Zhou), $k+2$ vertices (Slater, Teo and Yap), $k+3$ vertices (Wo\u017aniak) and $k+4$ vertices (Tiner). We further explore this direction. Given an arbitrary integer $c\\geq 1$, we prove Erd\u0151s-S\u00f3s conjecture in the case when $G$ has $k+c$ vertices provided that $k\\geq k_0(c)$ (here $k_0(c)=c^{12}{\\rm polylog}(c)$). We also derive a corollary related to the Tree Packing Conjecture.<\/jats:p>","DOI":"10.37236\/5405","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:34:18Z","timestamp":1578692058000},"source":"Crossref","is-referenced-by-count":5,"title":["On Erd\u0151s-S\u00f3s Conjecture for Trees of Large Size"],"prefix":"10.37236","volume":"23","author":[{"given":"Agnieszka","family":"Goerlich","sequence":"first","affiliation":[]},{"given":"Andrzej","family":"\u017bak","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,3,18]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i1p52\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i1p52\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:30:52Z","timestamp":1579239052000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i1p52"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,3,18]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,1,11]]}},"URL":"https:\/\/doi.org\/10.37236\/5405","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,3,18]]},"article-number":"P1.52"}}