{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T13:43:08Z","timestamp":1771854188145,"version":"3.50.1"},"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>Bollob\u00e1s and Thomason (1985) proved that for each $k=k(n) \\in [1, n-1]$, with high probability, the random graph process, where edges are added to vertex set $V=[n]$ uniformly at random one after another, is such that the stopping time of having minimal degree $k$ is equal to the stopping time of becoming $k$-(vertex-)connected. We extend this result to the $d$-uniform random hypergraph process, where $k$ and $d$ are fixed. Consequently, for $m=\\frac{n}{d}(\\ln n +(k-1)\\ln \\ln n +c)$ and $p=(d-1)! \\frac{\\ln n + (k-1) \\ln \\ln n +c}{n^{d-1}}$, the probability that the random hypergraph models $H_d(n, m)$ and $H_d(n, p)$ are $k$-connected tends to $e^{-e^{-c}\/(k-1)!}.$<\/jats:p>","DOI":"10.37236\/4666","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:29:01Z","timestamp":1578702541000},"source":"Crossref","is-referenced-by-count":9,"title":["On the Strength of Connectedness of a Random Hypergraph"],"prefix":"10.37236","volume":"22","author":[{"given":"Daniel","family":"Poole","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,3,23]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p69\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p69\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:23:37Z","timestamp":1579256617000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i1p69"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,3,23]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2015,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/4666","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,3,23]]},"article-number":"P1.69"}}