{"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":1753893860717,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We consider connected components in $k$-uniform hypergraphs for the following notion of connectedness: given integers $k\\ge 2$ and $1\\le j \\le k-1$, two $j$-sets (of vertices) lie in the same $j$-component if there is a sequence of edges from one to the other such that consecutive edges intersect in at least $j$ vertices.We prove that certain collections of $j$-sets constructed during a breadth-first search process on $j$-components in a random $k$-uniform hypergraph are reasonably regularly distributed with high probability. We use this property to provide a short proof of the asymptotic size of the giant $j$-component shortly after it appears.<\/jats:p>","DOI":"10.37236\/7712","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T07:06:20Z","timestamp":1578639980000},"source":"Crossref","is-referenced-by-count":1,"title":["The Size of the Giant Component in Random Hypergraphs: a Short Proof"],"prefix":"10.37236","volume":"26","author":[{"given":"Oliver","family":"Cooley","sequence":"first","affiliation":[]},{"given":"Mihyun","family":"Kang","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7886-5368","authenticated-orcid":false,"given":"Christoph","family":"Koch","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,7,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i3p6\/7863","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i3p6\/7863","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:11:55Z","timestamp":1579234315000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i3p6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,5]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,7,4]]}},"URL":"https:\/\/doi.org\/10.37236\/7712","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2019,7,5]]},"article-number":"P3.6"}}