{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T21:23:01Z","timestamp":1768771381007,"version":"3.49.0"},"reference-count":6,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2019,6,4]],"date-time":"2019-06-04T00:00:00Z","timestamp":1559606400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2019,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>m<\/jats:italic>(<jats:italic>k<\/jats:italic>) denote the maximum number of edges in a non-extendable, intersecting <jats:italic>k<\/jats:italic>-graph. Erd\u0151s and Lov\u00e1sz proved that <jats:italic>m<\/jats:italic>(<jats:italic>k<\/jats:italic>) \u2264 <jats:italic>k<\/jats:italic><jats:sup><jats:italic>k<\/jats:italic><\/jats:sup>. For <jats:italic>k<\/jats:italic> \u2265 625 we prove <jats:italic>m<\/jats:italic>(<jats:italic>k<\/jats:italic>) &lt; <jats:italic>k<jats:sup>k<\/jats:sup><\/jats:italic>\u30fb<jats:italic>e<\/jats:italic><jats:sup>\u2212<jats:italic>k<\/jats:italic><jats:sup>1<jats:italic>\/<\/jats:italic>4<\/jats:sup><jats:italic>\/<\/jats:italic>6<\/jats:sup>.<\/jats:p>","DOI":"10.1017\/s0963548319000142","type":"journal-article","created":{"date-parts":[[2019,6,4]],"date-time":"2019-06-04T08:42:57Z","timestamp":1559637777000},"page":"733-739","source":"Crossref","is-referenced-by-count":10,"title":["A near-exponential improvement of a bound of Erd\u0151s and Lov\u00e1sz on maximal intersecting families"],"prefix":"10.1017","volume":"28","author":[{"given":"Peter","family":"Frankl","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2019,6,4]]},"reference":[{"key":"S0963548319000142_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(94)90108-2"},{"key":"S0963548319000142_ref5","first-page":"209","article-title":"On the minimax theorems of combinatorics (in Hungarian)","volume":"26","author":"Lov\u00e1sz","year":"1975","journal-title":"Mat. Lapok"},{"key":"S0963548319000142_ref4","unstructured":"[4] Gy\u00e1rf\u00e1s, A. (1977) Partition covers and blocking sets in hypergraphs (in Hungarian). Thesis, Studies of Computer and Automation Research Institute of Hungarian Academy of Sciences, 177."},{"key":"S0963548319000142_ref3","doi-asserted-by":"publisher","DOI":"10.1006\/jcta.1996.0035"},{"key":"S0963548319000142_ref2","first-page":"609","volume-title":"Infinite and Finite Sets: Proc. Colloq. Math. Soc. J\u00e1nos Bolyai, Keszthely, Hungary","year":"1974"},{"key":"S0963548319000142_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2016.11.001"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548319000142","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,11]],"date-time":"2019-09-11T07:51:20Z","timestamp":1568188280000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548319000142\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,6,4]]},"references-count":6,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2019,9]]}},"alternative-id":["S0963548319000142"],"URL":"https:\/\/doi.org\/10.1017\/s0963548319000142","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,6,4]]}}}