{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T06:40:58Z","timestamp":1773816058932,"version":"3.50.1"},"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 $n &gt; k &gt; 1$ be integers, $[n] = \\{1, \\ldots, n\\}$. Let $\\mathcal F$ be a family of $k$-subsets of $[n]$. The family $\\mathcal F$ is called intersecting if $F \\cap F' \\neq \\varnothing$ for all $F, F' \\in \\mathcal F$. It is called almost intersecting if it is not intersecting but to every $F \\in \\mathcal F$ there is at most one $F'\\in \\mathcal F$ satisfying $F \\cap F' = \\varnothing$. Gerbner et al. proved that if $n \\geq 2k + 2$ then $|\\mathcal F| \\leqslant {n - 1\\choose k - 1}$ holds for almost\u00a0 intersecting families. Our main result implies the considerably stronger and best possible bound $|\\mathcal F| \\leqslant {n - 1\\choose k - 1} - {n - k - 1\\choose k - 1} + 2$ for $n &gt; (2 + o(1))k$, $k\\ge 3$.<\/jats:p>","DOI":"10.37236\/9609","type":"journal-article","created":{"date-parts":[[2021,4,9]],"date-time":"2021-04-09T01:22:27Z","timestamp":1617931347000},"source":"Crossref","is-referenced-by-count":2,"title":["Almost Intersecting Families"],"prefix":"10.37236","volume":"28","author":[{"given":"Peter","family":"Frankl","sequence":"first","affiliation":[]},{"given":"Andrey","family":"Kupavskii","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2021,4,9]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i2p7\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i2p7\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,9]],"date-time":"2021-04-09T01:22:28Z","timestamp":1617931348000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v28i2p7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,9]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,4,9]]}},"URL":"https:\/\/doi.org\/10.37236\/9609","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,4,9]]},"article-number":"P2.7"}}