{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:15Z","timestamp":1753893855589,"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>Let $\\mathcal{H}=(V,\\mathcal{E})$ be an $r$-uniform hypergraph on $n$ vertices and fix a positive integer $k$ such that $1\\le k\\le r$. A $k$-matching of $\\mathcal{H}$ is a collection of edges $\\mathcal{M}\\subset \\mathcal{E}$ such that every subset of $V$ whose cardinality equals $k$ is contained in at most one element of $\\mathcal{M}$. The $k$-matching number of $\\mathcal{H}$ is the maximum cardinality of a $k$-matching. A well-known problem, posed by Erd\u0151s, asks for the maximum number of edges in an $r$-uniform hypergraph under constraints on its $1$-matching number. In this article we investigate the more general problem of determining the maximum number of edges in an $r$-uniform hypergraph on $n$ vertices subject to the constraint that its $k$-matching number is strictly less than $a$. The problem can also be seen as a generalization of the well-known $k$-intersection problem. We propose candidate hypergraphs for the solution of this problem, and show that the extremal hypergraph is among this candidate set when $n\\ge 4r\\binom{r}{k}^2\\cdot a$.<\/jats:p>","DOI":"10.37236\/7420","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T10:33:29Z","timestamp":1578652409000},"source":"Crossref","is-referenced-by-count":0,"title":["A Generalization of Erd\u0151s' Matching Conjecture"],"prefix":"10.37236","volume":"25","author":[{"given":"Christos","family":"Pelekis","sequence":"first","affiliation":[]},{"given":"Israel","family":"Rocha","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,5,11]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i2p21\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i2p21\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T23:33:48Z","timestamp":1579217628000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i2p21"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,11]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,4,13]]}},"URL":"https:\/\/doi.org\/10.37236\/7420","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,5,11]]},"article-number":"P2.21"}}