{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:41Z","timestamp":1753893821321,"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>In 1975, Lov\u00e1sz conjectured that any maximal intersecting family of $k$-sets has at most $\\lfloor(e-1)k!\\rfloor$ blocks, where $e$ is the base of the natural logarithm. This conjecture was disproved in 1996 by Frankl and his co-authors. In this short note, we reprove the result of Frankl et al. using a vastly simplified construction of maximal intersecting families with many blocks. This construction yields a maximal intersecting family $\\mathbb{G}_{k}$ of $k-$sets whose number of blocks is asymptotic to $e^{2}(\\frac{k}{2})^{k-1}$ as $k\\rightarrow\\infty$.<\/jats:p>","DOI":"10.37236\/5976","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T20:28:32Z","timestamp":1578688112000},"source":"Crossref","is-referenced-by-count":0,"title":["A New Construction of Non-Extendable Intersecting Families of Sets"],"prefix":"10.37236","volume":"23","author":[{"given":"Kaushik","family":"Majumder","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,8,19]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i3p28\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i3p28\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:17:06Z","timestamp":1579238226000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i3p28"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,8,19]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2016,7,8]]}},"URL":"https:\/\/doi.org\/10.37236\/5976","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,8,19]]},"article-number":"P3.28"}}