{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,21]],"date-time":"2025-06-21T04:06:04Z","timestamp":1750478764412,"version":"3.41.0"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2003,5,20]],"date-time":"2003-05-20T00:00:00Z","timestamp":1053388800000},"content-version":"unspecified","delay-in-days":19,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2003,5]]},"abstract":"<jats:p>In this paper we consider a random star <jats:inline-formula>$d$<\/jats:inline-formula>-process which begins with <jats:inline-formula>$n$<\/jats:inline-formula> isolated vertices, and in each step chooses randomly a vertex of current minimum degree <jats:inline-formula>$\\delta$<\/jats:inline-formula>, and connects it with <jats:inline-formula>$d - \\delta$<\/jats:inline-formula> random vertices of degree less than <jats:inline-formula>$d$<\/jats:inline-formula>. We show that, for <jats:inline-formula>$d \\geqslant 3$<\/jats:inline-formula>, the resulting final graph is connected with probability <jats:inline-formula>$1 - o(1)$<\/jats:inline-formula>, and moreover that, for suficiently large <jats:inline-formula>$d$<\/jats:inline-formula>, it is <jats:inline-formula>$d$<\/jats:inline-formula>-connected with probability <jats:inline-formula>$1 - o(1)$<\/jats:inline-formula>.<\/jats:p>","DOI":"10.1017\/s0963548302005357","type":"journal-article","created":{"date-parts":[[2003,5,22]],"date-time":"2003-05-22T08:58:54Z","timestamp":1053593934000},"page":"269-283","source":"Crossref","is-referenced-by-count":1,"title":["Connectedness of the Degree Bounded Star Process"],"prefix":"10.1017","volume":"12","author":[{"given":"CATHERINE","family":"GREENHILL","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ANDRZEJ","family":"RUCI\u0143SKI","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"NICHOLAS C.","family":"WORMALD","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2003,5,20]]},"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548302005357","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,20]],"date-time":"2025-06-20T19:55:20Z","timestamp":1750449320000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548302005357\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,5]]},"references-count":0,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2003,11]]}},"alternative-id":["S0963548302005357"],"URL":"https:\/\/doi.org\/10.1017\/s0963548302005357","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"type":"print","value":"0963-5483"},{"type":"electronic","value":"1469-2163"}],"subject":[],"published":{"date-parts":[[2003,5]]}}}