{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,29]],"date-time":"2024-03-29T23:32:58Z","timestamp":1711755178655},"reference-count":27,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2018,12,7]],"date-time":"2018-12-07T00:00:00Z","timestamp":1544140800000},"content-version":"am","delay-in-days":365,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#am"},{"start":{"date-parts":[[2017,12,7]],"date-time":"2017-12-07T00:00:00Z","timestamp":1512604800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/100000001","name":"NSF","doi-asserted-by":"publisher","award":["DMS 1001781 and 1700280","DMS 1301698"],"award-info":[{"award-number":["DMS 1001781 and 1700280","DMS 1301698"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100004807","name":"DFG","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100004807","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Random Struct Algorithms"],"published-print":{"date-parts":[[2018,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Szemer\u00e9di 's Regularity Lemma is a powerful tool in graph theory. It asserts that all large graphs admit bounded partitions of their edge sets, most classes of which consist of uniformly distributed edges. The original proof of this result was nonconstructive, and a constructive proof was later given by Alon, Duke, Lefmann, R\u00f6dl, and Yuster. Szemer\u00e9di's Regularity Lemma was extended to hypergraphs by various authors. Frankl and R\u00f6dl gave one such extension in the case of 3\u2010uniform hypergraphs, which was later extended to <jats:italic>k<\/jats:italic>\u2010uniform hypergraphs by R\u00f6dl and Skokan. W.T. Gowers gave another such extension, using a different concept of regularity than that of Frankl, R\u00f6dl, and Skokan. Here, we give a constructive proof of a regularity lemma for hypergraphs.<\/jats:p>","DOI":"10.1002\/rsa.20739","type":"journal-article","created":{"date-parts":[[2017,12,8]],"date-time":"2017-12-08T04:44:38Z","timestamp":1512708278000},"page":"301-353","source":"Crossref","is-referenced-by-count":4,"title":["An algorithmic hypergraph regularity lemma"],"prefix":"10.1002","volume":"52","author":[{"given":"Brendan","family":"Nagle","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics University of South Florida Tampa Florida"}]},{"given":"Vojt\u011bch","family":"R\u00f6dl","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science Emory University Atlanta Georgia"}]},{"given":"Mathias","family":"Schacht","sequence":"additional","affiliation":[{"name":"Fachbereich Mathematik, Universit\u00e4t Hamburg Hamburg Germany"}]}],"member":"311","published-online":{"date-parts":[[2017,12,7]]},"reference":[{"key":"e_1_2_11_2_1","doi-asserted-by":"publisher","DOI":"10.1006\/jagm.1994.1005"},{"key":"e_1_2_11_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-012-2657-4"},{"key":"e_1_2_11_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-009-2356-y"},{"key":"e_1_2_11_5_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539799351729"},{"issue":"1973","key":"e_1_2_11_6_1","first-page":"298","volume":"14","author":"Erd\u0151s P.","journal-title":"J. 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The regularity lemma and its applications in graph theory Theoretical aspects of computer science (Tehran 2000) Lecture Notes in Computer Science vol. 2292 Springer Berlin 2002 pp. 84\u2013112.https:\/\/doi.org\/10.1007\/3-540-45878-6_3. MR1966181","DOI":"10.1007\/3-540-45878-6_3"},{"key":"e_1_2_11_16_1","doi-asserted-by":"crossref","unstructured":"B.Nagleet al. Hypergraph regularity and quasi\u2010randomness Proceedings of the Twentieth Annual ACM\u2010SIAM Symposium on Discrete Algorithms SIAM Philadelphia PA 2009 pp. 227\u2013235. MR2809322","DOI":"10.1137\/1.9781611973068.26"},{"key":"e_1_2_11_17_1","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20117"},{"key":"e_1_2_11_18_1","doi-asserted-by":"crossref","unstructured":"B.Nagle V.R\u00f6dl andM.Schacht Extremal hypergraph problems and the regularity method Topics in discrete mathematics Algorithms and Combinetorics vol. 26 Springer Berlin 2006 pp. 247\u2013278.https:\/\/doi.org\/10.1007\/3-540-33700-8_16. MR2249275","DOI":"10.1007\/3-540-33700-8_16"},{"key":"e_1_2_11_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(88)90003-7"},{"key":"e_1_2_11_20_1","unstructured":"V.R\u00f6dl Quasi\u2010randomness and the regularity method in hypergraphs Proceedings of the International Congress of Mathematicians vol. I (Seoul 2014) KM Kyung Moon Sa Seoul pp.573\u2013601."},{"key":"e_1_2_11_21_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0502771102"},{"key":"e_1_2_11_22_1","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20017"},{"key":"e_1_2_11_23_1","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20056"},{"key":"e_1_2_11_24_1","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20108"},{"key":"e_1_2_11_25_1","unstructured":"J.Spencer Ten lectures on the probabilistic method CBMS\u2010NSF Regional Conference Series in Applied Mathematics vol. 52 Society for Industrial and Applied Mathematics (SIAM) Philadelphia PA 1987. 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