{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:20Z","timestamp":1753893860732,"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>We consider the following definition of connectedness in $k$-uniform hypergraphs: two $j$-sets (sets of $j$ vertices) are $j$-connected if there is a walk of edges between them such that two consecutive edges intersect in at least $j$ vertices. The hypergraph is $j$-connected if all $j$-sets are pairwise $j$-connected. We determine the threshold at which the random $k$-uniform hypergraph with edge probability $p$ becomes $j$-connected with high probability. We also deduce a hitting time result for the random hypergraph process \u2013\u00a0the hypergraph becomes $j$-connected at exactly the moment when the last isolated $j$-set disappears. This generalises the classical hitting time result of Bollob\u00e1s and Thomason for graphs.<\/jats:p>","DOI":"10.37236\/5064","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:01:44Z","timestamp":1578690104000},"source":"Crossref","is-referenced-by-count":5,"title":["Threshold and Hitting Time for High-Order Connectedness in Random Hypergraphs"],"prefix":"10.37236","volume":"23","author":[{"given":"Oliver","family":"Cooley","sequence":"first","affiliation":[]},{"given":"Mihyun","family":"Kang","sequence":"additional","affiliation":[]},{"given":"Christoph","family":"Koch","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,6,10]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i2p48\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i2p48\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:27:56Z","timestamp":1579238876000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i2p48"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,6,10]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2016,3,31]]}},"URL":"https:\/\/doi.org\/10.37236\/5064","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,6,10]]},"article-number":"P2.48"}}