{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:49Z","timestamp":1753893829112,"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>We study the joint components in a random 'double graph' that is obtained by superposing red and blue binomial random graphs on $n$~vertices. \u00a0A joint component is a maximal set of vertices that supports both a red and a blue spanning tree. \u00a0We show that there are critical pairs of red and blue edge densities at which a giant joint component appears.\u00a0 In contrast to the standard binomial graph model, the phase transition is first order:\u00a0 the size of the largest joint component jumps from $O(1)$ vertices to $\\Theta(n)$ at the critical point.\u00a0 We connect this phenomenon to the properties of a certain bicoloured branching process.\u00a0<\/jats:p>","DOI":"10.37236\/8846","type":"journal-article","created":{"date-parts":[[2021,2,11]],"date-time":"2021-02-11T10:11:37Z","timestamp":1613038297000},"source":"Crossref","is-referenced-by-count":0,"title":["The Size of the Giant Joint Component in a Binomial Random Double Graph"],"prefix":"10.37236","volume":"28","author":[{"given":"Mark","family":"Jerrum","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tam\u00e1s","family":"Makai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2021,2,12]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i1p33\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i1p33\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,11]],"date-time":"2021-02-11T10:11:37Z","timestamp":1613038297000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v28i1p33"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,12]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,1,14]]}},"URL":"https:\/\/doi.org\/10.37236\/8846","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2021,2,12]]},"article-number":"P1.33"}}