{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,22]],"date-time":"2025-08-22T02:10:59Z","timestamp":1755828659312,"version":"3.44.0"},"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>Using the sunflower method, we show that if $\\theta \\in (0,1) \\cap \\mathbb{Q}$ and $\\mathcal{F}$ is a $O(n^{1\/3})$-bounded $\\theta$-intersecting family over $[n]$, then $\\lvert \\mathcal{F} \\rvert = O(n)$, and that if $\\mathcal{F}$ is $o(n^{1\/3})$-bounded, then $\\lvert \\mathcal{F} \\rvert \\leq (\\frac{3}{2} + o(1))n$. This partially solves a conjecture of Balachandran, Mathew and Mishra\u00a0that any $\\theta$-intersecting family over $[n]$ has size at most linear in $n$, in the regime where we have no very large sets.<\/jats:p>","DOI":"10.37236\/12900","type":"journal-article","created":{"date-parts":[[2025,8,21]],"date-time":"2025-08-21T14:04:58Z","timestamp":1755785098000},"source":"Crossref","is-referenced-by-count":0,"title":["Bounded Fractional Intersecting Families are Linear in Size"],"prefix":"10.37236","volume":"32","author":[{"given":"Niranjan","family":"Balachandran","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shagnik","family":"Das","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Brahadeesh","family":"Sankarnarayanan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2025,8,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i3p34\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i3p34\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,21]],"date-time":"2025-08-21T14:04:58Z","timestamp":1755785098000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v32i3p34"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,22]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,7,4]]}},"URL":"https:\/\/doi.org\/10.37236\/12900","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2025,8,22]]},"article-number":"P3.34"}}