{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:09:34Z","timestamp":1758823774395,"version":"3.41.2"},"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>In 1990 Erd\u0151s, Faudree, Rousseau and Schelp proved that for $k \\ge 2$, every graph with $n \\ge k+1$ vertices and $(k-1)(n-k+2)+\\binom{k-2}{2}+1$ edges contains a subgraph of minimum degree $k$ on at most $n-\\sqrt{n\/6k^3}$ vertices. They conjectured that it is possible to remove at least $\\epsilon_k n$ many vertices and remain with a subgraph of minimum degree $k$, for some $\\epsilon_k&gt;0$. We make progress towards their conjecture by showing that one can remove at least order of $\\Omega(n\/\\log n)$ many vertices.<\/jats:p>","DOI":"10.37236\/7167","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:44:46Z","timestamp":1578671086000},"source":"Crossref","is-referenced-by-count":1,"title":["Smaller Subgraphs of Minimum Degree $k$"],"prefix":"10.37236","volume":"24","author":[{"given":"Frank","family":"Mousset","sequence":"first","affiliation":[]},{"given":"Andreas","family":"Noever","sequence":"additional","affiliation":[]},{"given":"Nemanja","family":"\u0160kori\u0107","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2017,10,6]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i4p9\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i4p9\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:45:06Z","timestamp":1579236306000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i4p9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,10,6]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2017,10,5]]}},"URL":"https:\/\/doi.org\/10.37236\/7167","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2017,10,6]]},"article-number":"P4.9"}}