{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T16:03:32Z","timestamp":1773245012032,"version":"3.50.1"},"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>For a graph $G=(V,E)$ of even order, a partition $(V_1,V_2)$ of the vertices is said to be perfectly balanced if $|V_1|=|V_2|$ and the numbers of edges in the subgraphs induced by $V_1$ and $V_2$ are equal. For a base graph $H$ define a random graph $G(H,p)$ by turning every non-edge of $H$ into an edge and every edge of $H$ into a non-edge independently with probability $p$. We show that for any constant $\\epsilon$ there is a constant $\\alpha$, such that for any even $n$ and a graph $H$ on $n$ vertices that satisfies $\\Delta(H)-\\delta(H) \\leq \\alpha n$, a graph $G$ distributed according to $G(H,p)$, with ${\\epsilon\\over n} \\leq p \\leq 1-{\\epsilon\\over n}$, admits a perfectly balanced partition with probability exponentially close to $1$. As a direct consequence we get that for every $p$, a random graph from $G(n,p)$ admits a perfectly balanced partition with probability tending to $1$.<\/jats:p>","DOI":"10.37236\/252","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:31:38Z","timestamp":1578717098000},"source":"Crossref","is-referenced-by-count":4,"title":["Perfectly Balanced Partitions of Smoothed Graphs"],"prefix":"10.37236","volume":"16","author":[{"given":"Ido","family":"Ben-Eliezer","sequence":"first","affiliation":[]},{"given":"Michael","family":"Krivelevich","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,5,11]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1n14\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1n14\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T02:55:25Z","timestamp":1579316125000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1n14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,5,11]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/252","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,5,11]]},"article-number":"N14"}}