{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T16:50:33Z","timestamp":1781196633126,"version":"3.54.1"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2016,2,1]],"date-time":"2016-02-01T00:00:00Z","timestamp":1454284800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Combinatorica"],"published-print":{"date-parts":[[2016,12]]},"DOI":"10.1007\/s00493-014-3133-0","type":"journal-article","created":{"date-parts":[[2016,2,1]],"date-time":"2016-02-01T08:53:13Z","timestamp":1454316793000},"page":"623-660","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["The minimum number of disjoint pairs in set systems and related problems"],"prefix":"10.1007","volume":"36","author":[{"given":"Shagnik","family":"Das","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenying","family":"Gan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Benny","family":"Sudakov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2016,2,1]]},"reference":[{"key":"3133_CR1","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/0095-8956(80)90062-3","volume":"28","author":"R. Ahlswede","year":"1980","unstructured":"R. Ahlswede: Simple hypergraphs with maximal number of adjacent pairs of edges, J. Combinatorial Theory (B) 28 (1980), 164\u2013167.","journal-title":"J. Combinatorial Theory (B)"},{"key":"3133_CR2","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1017\/S0963548399003909","volume":"8","author":"R. Ahlswede","year":"1999","unstructured":"R. Ahlswede and N. Cai: A counterexample to Kleitman's conjecture concerning an edge-isoperimetric problem, Combinatorics, Probability and Computing 8 (1999), 301\u2013305.","journal-title":"Combinatorics, Probability and Computing"},{"key":"3133_CR3","doi-asserted-by":"crossref","first-page":"979","DOI":"10.1007\/11889342_63","volume-title":"General Theory of Information Transfer and Combinatorics","author":"R. Ahlswede","year":"2006","unstructured":"R. Ahlswede and N. Cai: Appendix: on edge-isoperimetric theorems for uniform hypergraphs, General Theory of Information Transfer and Combinatorics, Springer Berlin Heidelberg (2006), 979\u20131005."},{"key":"3133_CR4","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/BF01902206","volume":"32","author":"R. Ahlswede","year":"1978","unstructured":"R. Ahlswede and G. O. H. Katona: Graphs with maximal number of adjacent pairs of edges, Acta Mathematica Hungarica 32 (1978), 97\u2013120.","journal-title":"Acta Mathematica Hungarica"},{"key":"3133_CR5","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1006\/eujc.1995.0092","volume":"18","author":"R. Ahlswede","year":"1997","unstructured":"R. Ahlswede and L. H. Khachatrian: The complete intersection theorem for systems of nite sets, European Journal of Combinatorics 18 (1997), 125\u2013136.","journal-title":"European Journal of Combinatorics"},{"key":"3133_CR6","volume-title":"Courier Dover Publications","author":"I. Anderson","year":"1987","unstructured":"I. Anderson: Combinatorics of Finite Sets, Courier Dover Publications, 1987."},{"key":"3133_CR7","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1007\/s00493-003-0033-0","volume":"23","author":"B. Bollob\u00e1s","year":"2003","unstructured":"B. Bollob\u00e1s and I. Leader: Set systems with few disjoint pairs, Combinatorica 23 (2003), 559\u2013570.","journal-title":"Combinatorica"},{"key":"3133_CR8","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1016\/0097-3165(88)90034-9","volume":"49","author":"F. R. K. Chung","year":"1988","unstructured":"F. R. K. Chung, Z. F\u00fcredi, R. L. Graham and P. Seymour: On induced subgraphs of the cube, J. Combinatorial Theory (A) 49 (1988), 180\u2013187.","journal-title":"J. Combinatorial Theory (A)"},{"key":"3133_CR9","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1017\/S0963548314000273","volume":"24","author":"S. Das","year":"2015","unstructured":"S. Das, W. Gan and B. Sudakov: Sperner's theorem and a problem of Erdos, Katona and Kleitman, Combinatorics, Probability and Computing 24 (2015), 585\u2013608.","journal-title":"Probability and Computing"},{"key":"3133_CR10","first-page":"#A4","volume":"14A","author":"A. P. Dove","year":"2014","unstructured":"A. P. Dove, J. R. Griggs, R. J. Kang and J. S. Sereni: Supersaturation in the Boolean lattice, Integers 14A (2014), #A4.","journal-title":"Integers"},{"key":"3133_CR11","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1215\/ijm\/1255631811","volume":"6","author":"P. Erd\u0151s","year":"1962","unstructured":"P. Erd\u0151s: On a theorem of Rademacher-Turan, Illinois Journal of Math 6 (1962), 122\u2013127.","journal-title":"Illinois Journal of Math"},{"key":"3133_CR12","first-page":"459","volume":"7","author":"P. Erd\u0151s","year":"1962","unstructured":"P. Erd\u0151s: On the number of complete subgraphs contained in certain graphs, Magy. Tud. Akad. Mat. Kut. Int. K\u00f6zl. 7 (1962), 459\u2013474.","journal-title":"Magy. Tud. Akad. Mat. Kut. Int. K\u00f6zl."},{"key":"3133_CR13","first-page":"93","volume":"8","author":"P. Erd\u0151s","year":"1965","unstructured":"P. Erd\u0151s: A problem on independent r-tuples, Ann. Univ. Sci. Budapest. E\u00f6tv\u00f6s Sect. Math. 8 (1965), 93\u201395.","journal-title":"Ann. Univ. Sci. Budapest. E\u00f6tv\u00f6s Sect. Math."},{"key":"3133_CR14","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1093\/qmath\/12.1.313","volume":"12","author":"P. Erd\u0151s","year":"1961","unstructured":"P. Erd\u0151s, C. Ko and R. Rado: Intersection theorems for systems of finite sets, The Quarterly Journal of Mathematics 12 (1961), 313\u2013320.","journal-title":"The Quarterly Journal of Mathematics"},{"key":"3133_CR15","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/0097-3165(77)90056-5","volume":"22","author":"P. Frankl","year":"1977","unstructured":"P. Frankl: On the minimum number of disjoint pairs in a family of finite sets, J. Combinatorial Theory (A) 22 (1977), 249\u2013251.","journal-title":"J. Combinatorial Theory (A)"},{"key":"3133_CR16","doi-asserted-by":"crossref","first-page":"1068","DOI":"10.1016\/j.jcta.2013.01.008","volume":"120","author":"P. Frankl","year":"2013","unstructured":"P. Frankl: Improved bounds for Erd\u0151s' Matching Conjecture, J. Combinatorial Theory (A) 120 (2013), 1068\u20131072.","journal-title":"J. Combinatorial Theory (A)"},{"key":"3133_CR17","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1017\/S0963548311000496","volume":"21","author":"P. Frankl","year":"2012","unstructured":"P. Frankl, V. R\u00f6dl and A. Rucinski: On the maximum number of edges in a triple system not containing a disjoint family of a given size, Combinatorics, Probability and Computing 21 (2012), 141\u2013148.","journal-title":"Probability and Computing"},{"key":"3133_CR18","doi-asserted-by":"crossref","first-page":"1657","DOI":"10.1137\/120878744","volume":"26","author":"D. Gerbner","year":"2012","unstructured":"D. Gerbner, N. Lemons, C. Palmer, B. Patk\u00f3s and V. Sz\u00e9csi: Almost intersecting families of sets, SIAM Journal of Discrete Math. 26 (2012), 1657\u20131669.","journal-title":"SIAM Journal of Discrete Math."},{"key":"3133_CR19","doi-asserted-by":"crossref","first-page":"442","DOI":"10.1017\/S096354831100068X","volume":"21","author":"H. Huang","year":"2012","unstructured":"H. Huang, P. Loh and B. Sudakov: The size of a hypergraph and its matching number, Combinatorics, Probability and Computing 21 (2012), 442\u2013450.","journal-title":"Probability and Computing"},{"key":"3133_CR20","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1017\/S0963548311000587","volume":"21","author":"G. O. H. Katona","year":"2012","unstructured":"G. O. H. Katona, G. Y. Katona and Zs. Katona: Most probably intersecting families of subsets, Combinatorics, Probability and Computing 21 (2012), 219\u2013227.","journal-title":"Probability and Computing"},{"key":"3133_CR21","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/j.jcta.2014.01.003","volume":"124","author":"T. Luczak","year":"2014","unstructured":"T. Luczak and K. Mieczkowska: On Erd\u0151s' extremal problem on matchings in hypergraphs, J. Combinatorial Theory (A) 124 (2014), 178\u2013194","journal-title":"J. Combinatorial Theory (A)"},{"key":"3133_CR22","first-page":"60","volume":"10","author":"W. Mantel","year":"1907","unstructured":"W. Mantel: Problem 28, Winkundige Opgaven 10 (1907), 60\u201361.","journal-title":"Winkundige Opgaven"},{"key":"3133_CR23","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1007\/BF01788540","volume":"3","author":"S. Poljak","year":"1987","unstructured":"S. Poljak and Zs. Tuza: Maximum bipartite subgraphs of Kneser graphs, Graphs and Combinatorics 3 (1987), 191\u2013199.","journal-title":"Graphs and Combinatorics"},{"key":"3133_CR24","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1007\/BF02579226","volume":"4","author":"R. M. Wilson","year":"1984","unstructured":"R. M. Wilson: The exact bound on the Erd\u0151s-Ko-Rado Theorem, Combinatorica 4 (1984), 247\u2013257.","journal-title":"Combinatorica"}],"container-title":["Combinatorica"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-014-3133-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00493-014-3133-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-014-3133-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-014-3133-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,4]],"date-time":"2019-09-04T01:06:55Z","timestamp":1567559215000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00493-014-3133-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,2,1]]},"references-count":24,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2016,12]]}},"alternative-id":["3133"],"URL":"https:\/\/doi.org\/10.1007\/s00493-014-3133-0","relation":{},"ISSN":["0209-9683","1439-6912"],"issn-type":[{"value":"0209-9683","type":"print"},{"value":"1439-6912","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,2,1]]}}}