{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:27Z","timestamp":1753893807127,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>There has been much recent interest in random graphs sampled uniformly from the n-vertex graphs in a suitable\u00a0minor-closed class, such as the class of all planar graphs. Here we use combinatorial and probabilistic methods to investigate a more general model.\u00a0We consider random graphs from a 'well-behaved' class of graphs: examples of such classes include all minor-closed classes of graphs with 2-connected excluded minors (such as forests, series-parallel graphs and planar graphs), the class of graphs embeddable on any given surface, and the class of graphs with at most $k$ vertex-disjoint cycles.\u00a0 Also, we give weights to edges and components to specify\u00a0probabilities, so that our random graphs correspond to the random cluster model, appropriately conditioned.We find that earlier results extend naturally in both directions, to general well-behaved classes of graphs, and to the weighted framework,\u00a0for example results concerning the probability of a random graph being connected; and we also give results on the 2-core which are new even for the uniform (unweighted) case.<\/jats:p>","DOI":"10.37236\/2793","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:31:58Z","timestamp":1578706318000},"source":"Crossref","is-referenced-by-count":3,"title":["Random Graphs from a Weighted Minor-Closed Class"],"prefix":"10.37236","volume":"20","author":[{"given":"Colin","family":"McDiarmid","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,6,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i2p52\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i2p52\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:18:53Z","timestamp":1579259933000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i2p52"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,6,7]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2013,4,9]]}},"URL":"https:\/\/doi.org\/10.37236\/2793","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,6,7]]},"article-number":"P52"}}