{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:29Z","timestamp":1753893809564,"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>Let $h$ be a given positive integer. For a graph with $n$ vertices and $m$ edges, what is the maximum number of pairwise edge-disjoint {\\em induced} subgraphs, each having\u00a0 minimum degree at least $h$? There are examples for which this number is $O(m^2\/n^2)$. We prove that this bound is achievable for all graphs with polynomially many edges. For all $\\epsilon &gt; 0$, if $m \\ge n^{1+\\epsilon}$, then there are always $\\Omega(m^2\/n^2)$ pairwise edge-disjoint induced subgraphs, each having\u00a0 minimum degree at least $h$. Furthermore, any two subgraphs intersect in an independent set of size at most $1+ O(n^3\/m^2)$, which is shown to be asymptotically optimal.<\/jats:p>","DOI":"10.37236\/2882","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:57:19Z","timestamp":1578693439000},"source":"Crossref","is-referenced-by-count":1,"title":["Edge-Disjoint Induced Subgraphs with Given Minimum Degree"],"prefix":"10.37236","volume":"20","author":[{"given":"Raphael","family":"Yuster","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2013,3,8]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p53\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p53\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T06:25:35Z","timestamp":1579242335000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i1p53"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,3,8]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2013,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/2882","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,3,8]]},"article-number":"P53"}}