{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,12]],"date-time":"2025-09-12T17:57:21Z","timestamp":1757699841407},"reference-count":10,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":4089,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Random Struct Algorithms"],"published-print":{"date-parts":[[1995,8]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>E = {X<\/jats:italic><jats:sub>1<\/jats:sub>, <jats:italic>X<\/jats:italic><jats:sub>2<\/jats:sub>\u2026, <jats:italic>X<jats:sub>m<\/jats:sub><\/jats:italic>} where the <jats:italic>X<jats:sub>i<\/jats:sub><\/jats:italic> \u2286 <jats:italic>V<\/jats:italic> for 1 \u2264 <jats:italic>i<\/jats:italic> \u2264 <jats:italic>m<\/jats:italic> are distinct. The hypergraph <jats:italic>G<\/jats:italic> = (<jats:italic>V, E<\/jats:italic>) is said to be <jats:italic>s\u2010uniform<\/jats:italic> if |<jats:italic>X<\/jats:italic><jats:sub>1<\/jats:sub>| = <jats:italic>s<\/jats:italic> for 1 \u2264 <jats:italic>i<\/jats:italic> \u2264 <jats:italic>m.<\/jats:italic> A set of edges <jats:italic>M<\/jats:italic> = {<jats:italic>X<jats:sub>i<\/jats:sub><\/jats:italic> : <jats:italic>i<\/jats:italic> \u03f5 <jats:bold><jats:italic>I<\/jats:italic><\/jats:bold>} is a <jats:italic>perfect matching<\/jats:italic> if (i) <jats:italic>i<\/jats:italic> \u2260 <jats:italic>j<\/jats:italic> \u03f5 <jats:bold><jats:italic>I<\/jats:italic><\/jats:bold> implies <jats:italic>X<jats:sub>i<\/jats:sub><\/jats:italic> \u2229 <jats:italic>X<jats:sub>i<\/jats:sub><\/jats:italic> = 0, and (ii) \u222a<jats:sub><jats:italic>i<\/jats:italic>\u03f5<jats:italic>I<\/jats:italic><\/jats:sub> <jats:italic>X<jats:sub>i<\/jats:sub><\/jats:italic> = <jats:italic>V<\/jats:italic>.<\/jats:p><jats:p>In this article we consider the question of whether a random <jats:italic>s<\/jats:italic>\u2010uniform hypergraph contains a perfect matching. Let <jats:italic>s<\/jats:italic> \u2265 3 be fixed and <jats:italic>m\/n<\/jats:italic><jats:sup>4\/3<\/jats:sup> \u2192 \u221e. We show that an <jats:italic>s<\/jats:italic>\u2010uniform hypergraph with <jats:italic>m<\/jats:italic> edges chosen uniformly from [74] contains a perfect matching with high probability. This improves an earlier result of Schmidt and Shamir who showed that <jats:italic>m\/n<\/jats:italic><jats:sup>3\/2<\/jats:sup> \u2192 \u221e suffices. \u00a9 1995 John Wiley &amp; Sons, Inc.<\/jats:p>","DOI":"10.1002\/rsa.3240070104","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T18:49:30Z","timestamp":1180205370000},"page":"41-57","source":"Crossref","is-referenced-by-count":18,"title":["Perfect matchings in random s\u2010uniform hypergraphs"],"prefix":"10.1002","volume":"7","author":[{"given":"Alan","family":"Frieze","sequence":"first","affiliation":[]},{"given":"Svante","family":"Janson","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(78)90059-6"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0195-6698(80)80030-8"},{"key":"e_1_2_1_4_2","first-page":"23","article-title":"On matchings and hamiltonian cycles in random graphs","volume":"28","author":"Bollob\u00e1s B.","year":"1985","journal-title":"Ann. Discrete Math."},{"key":"e_1_2_1_5_2","doi-asserted-by":"crossref","unstructured":"B.Bollob\u00e1s T. I.Fenner andA. M.Frieze Hamilton cycles in random graphs with minimal degree at least k inA Tribute to Paul Erd\u00f5s A. Baker B. Bollob\u00e1s and A. Hajnal Eds. 1990 pp.59\u201396.","DOI":"10.1017\/CBO9780511983917.006"},{"key":"e_1_2_1_6_2","article-title":"Perfect matchings in random r\u2010regular, s\u2010uniform hypergraphs","author":"Cooper C.","journal-title":"Combinat. Probab. Comput."},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01894879"},{"key":"e_1_2_1_8_2","article-title":"The numbers of spanning trees, Hamilton cycles and perfect matchings in a random graph","author":"Janson S.","journal-title":"Combinat. Probab. Comput."},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.3240030202"},{"key":"e_1_2_1_10_2","article-title":"Almost all regular graphs are Hamiltonian","author":"Robinson R. W.","journal-title":"Random Struct. Alg."},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(83)90044-4"}],"container-title":["Random Structures &amp; Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Frsa.3240070104","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/rsa.3240070104","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T05:37:57Z","timestamp":1698298677000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/rsa.3240070104"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,8]]},"references-count":10,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1995,8]]}},"alternative-id":["10.1002\/rsa.3240070104"],"URL":"https:\/\/doi.org\/10.1002\/rsa.3240070104","archive":["Portico"],"relation":{},"ISSN":["1042-9832","1098-2418"],"issn-type":[{"value":"1042-9832","type":"print"},{"value":"1098-2418","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,8]]}}}