{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:48Z","timestamp":1753893828637,"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>Generate a bipartite graph on a partitioned set of vertices by randomly assigning to each vertex $v$ some weight $w(v) \\in [0,1]$ and adding\u00a0an edge between vertices $u$ and $v$ (in distinct parts) if and only if $w(v) + w(v) &gt; 1$; the results of such processes are known as difference graphs.Random difference graphs of a given size can be produced either\u00a0by uniformly random generation of weights or by choosing a graph\u00a0uniformly at random from the set of all such graphs. We prove that\u00a0these two methods give rise to the same distribution, and use this\u00a0equivalence to find exact results for the likelihood of connectivity and\u00a0Hamiltonicity. We also find the distribution of other properties, such\u00a0as matching number and degeneracy.<\/jats:p>","DOI":"10.37236\/2354","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:11:25Z","timestamp":1578712285000},"source":"Crossref","is-referenced-by-count":0,"title":["Properties of Random Difference Graphs"],"prefix":"10.37236","volume":"19","author":[{"given":"Christopher","family":"Ross","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2012,11,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i4p28\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i4p28\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:22:51Z","timestamp":1579299771000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v19i4p28"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,11,22]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2012,10,18]]}},"URL":"https:\/\/doi.org\/10.37236\/2354","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2012,11,22]]},"article-number":"P28"}}