{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:25:43Z","timestamp":1759335943274,"version":"3.41.2"},"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>A simple matrix is a (0,1)-matrix with no repeated columns. For a (0,1)-matrix $F$, we say\u00a0that a (0,1)-matrix $A$ has $F$ as a Berge hypergraph if there is a submatrix $B$ of $A$ and some row and column permutation of $F$, say $G$, with $G\\le B$. Letting $\\|A\\|$ denote the number of columns in $A$, we define the extremal function $\\mathrm{Bh}(m,{ F})=\\max\\{\\|A\\|\\,:\\, A \\hbox{ }m\\hbox{-rowed simple matrix and no Berge hypergraph }F\\}$. We determine the asymptotics of $\\mathrm{Bh}(m,F)$ for all $3$- and $4$-rowed $F$ and most $5$-rowed $F$. For certain $F$, this becomes the problem of determining the maximum number of copies of $K_r$ in a $m$-vertex graph that has no $K_{s,t}$ subgraph, a problem studied by Alon and Shikhelman.<\/jats:p>","DOI":"10.37236\/6482","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:58:45Z","timestamp":1578671925000},"source":"Crossref","is-referenced-by-count":4,"title":["Forbidden Berge Hypergraphs"],"prefix":"10.37236","volume":"24","author":[{"given":"R. P.","family":"Anstee","sequence":"first","affiliation":[]},{"given":"Santiago","family":"Salazar","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2017,3,31]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i1p59\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i1p59\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:02:54Z","timestamp":1579237374000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i1p59"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3,31]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2017,1,20]]}},"URL":"https:\/\/doi.org\/10.37236\/6482","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2017,3,31]]},"article-number":"P1.59"}}