{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:11Z","timestamp":1753893851180,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A set $S$ of vertices in a hypergraph $H$ is a transversal if it has a nonempty intersection with every edge of $H$. The upper transversal number $\\Upsilon(H)$ of $H$ is the maximum cardinality of a minimal transversal in $H$. We show that if $H$ is a connected $3$-uniform hypergraph of order $n$, then $\\Upsilon(H) &gt; 1.4855 \\sqrt[3]{n} - 2$. For $n$ sufficiently large, we construct infinitely many connected $3$-uniform hypergraphs, $H$, of order~$n$ satisfying $\\Upsilon(H) &lt; 2.5199 \\sqrt[3]{n}$. We conjecture that $\\displaystyle{\\sup_{n \\to \\infty}\u00a0 \\, \\left( \\inf\u00a0 \\frac{ \\Upsilon(H) }{ \\sqrt[3]{n} } \\right) = \\sqrt[3]{16} }$, where the infimum is taken over all connected $3$-uniform hypergraphs $H$ of order $n$.<\/jats:p>","DOI":"10.37236\/7267","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T10:04:38Z","timestamp":1578650678000},"source":"Crossref","is-referenced-by-count":3,"title":["On Upper Transversals in 3-Uniform Hypergraphs"],"prefix":"10.37236","volume":"25","author":[{"given":"Michael A.","family":"Henning","sequence":"first","affiliation":[]},{"given":"Anders","family":"Yeo","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,11,2]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i4p27\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i4p27\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T23:22:01Z","timestamp":1579216921000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i4p27"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,2]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,10,5]]}},"URL":"https:\/\/doi.org\/10.37236\/7267","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,11,2]]},"article-number":"P4.27"}}