{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,5,20]],"date-time":"2024-05-20T09:54:54Z","timestamp":1716198894633},"reference-count":2,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2008,9,12]],"date-time":"2008-09-12T00:00:00Z","timestamp":1221177600000},"content-version":"unspecified","delay-in-days":5947,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[1992,6]]},"abstract":"<jats:p>For a graph <jats:italic>G<\/jats:italic> with <jats:italic>m<\/jats:italic> edges let its Range of Subgraph Sizes (RSS)<\/jats:p><jats:p>\u03c1(<jats:italic>G<\/jats:italic>) = {<jats:italic>t<\/jats:italic> : <jats:italic>G<\/jats:italic> contains a vertex-induced subgraph with <jats:italic>t<\/jats:italic> edges}.<\/jats:p><jats:p><jats:italic>G<\/jats:italic> has a <jats:italic>full<\/jats:italic> RSS if \u03c1(<jats:italic>G<\/jats:italic>) = {0, 1, \u2026, <jats:italic>m<\/jats:italic>}. We establish the threshold for a random graph to have a full RSS and give tight bounds on the likely RSS of a dense random graph.<\/jats:p>","DOI":"10.1017\/s0963548300000146","type":"journal-article","created":{"date-parts":[[2008,9,12]],"date-time":"2008-09-12T11:20:14Z","timestamp":1221218414000},"page":"123-134","source":"Crossref","is-referenced-by-count":7,"title":["On Subgraph Sizes in Random Graphs"],"prefix":"10.1017","volume":"1","author":[{"given":"Neil","family":"Calkin","sequence":"first","affiliation":[]},{"given":"Alan","family":"Frieze","sequence":"additional","affiliation":[]},{"given":"Brendan D.","family":"McKay","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2008,9,12]]},"reference":[{"key":"S0963548300000146_ref001","volume-title":"Random Graphs","author":"Bollob\u00e1s","year":"1985"},{"key":"S0963548300000146_ref002","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.3240010102"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548300000146","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T21:37:33Z","timestamp":1558042653000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548300000146\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,6]]},"references-count":2,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1992,6]]}},"alternative-id":["S0963548300000146"],"URL":"https:\/\/doi.org\/10.1017\/s0963548300000146","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,6]]}}}