{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T12:32:46Z","timestamp":1772368366188,"version":"3.50.1"},"reference-count":25,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2013,8,23]],"date-time":"2013-08-23T00:00:00Z","timestamp":1377216000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[2014,7]]},"abstract":"Abstract<\/jats:title>For a graph G<\/jats:italic>, let be the probability that three distinct random vertices span exactly i<\/jats:italic> edges. We call the 3\u2010local profile<\/jats:italic>\nof G<\/jats:italic>. We investigate the set of all vectors that are arbitrarily close to the 3\u2010local profiles of arbitrarily large graphs. We give a full description of the projection of to the plane. The upper envelope of this planar domain is obtained from cliques on a fraction of the vertex set and complements of such graphs. The lower envelope is Goodman's inequality . We also give a full description of the triangle\u2010free case, i.e. the intersection of with the hyperplane . This planar domain is characterized by an SDP constraint that is derived from Razborov's flag algebra theory.<\/jats:p>","DOI":"10.1002\/jgt.21762","type":"journal-article","created":{"date-parts":[[2013,8,23]],"date-time":"2013-08-23T20:36:53Z","timestamp":1377290213000},"page":"236-248","source":"Crossref","is-referenced-by-count":11,"title":["On the 3\u2010Local Profiles of Graphs"],"prefix":"10.1002","volume":"76","author":[{"given":"Hao","family":"Huang","sequence":"first","affiliation":[{"name":"SCHOOL OF MATHEMATICS INSTITUTE FOR ADVANCED STUDY PRINCETON NJ 08540"}]},{"given":"Nati","family":"Linial","sequence":"additional","affiliation":[{"name":"SCHOOL OF COMPUTER SCIENCE AND ENGINEERING THE HEBREW UNIVERSITY OF JERUSALEM JERUSALEM 91904 ISRAEL"}]},{"given":"Humberto","family":"Naves","sequence":"additional","affiliation":[{"name":"DEPARTMENT OF MATHEMATICS UCLA, LOS ANGELES CA 90095"}]},{"given":"Yuval","family":"Peled","sequence":"additional","affiliation":[{"name":"SCHOOL OF COMPUTER SCIENCE AND ENGINEERING THE HEBREW UNIVERSITY OF JERUSALEM JERUSALEM 91904 ISRAEL"}]},{"given":"Benny","family":"Sudakov","sequence":"additional","affiliation":[{"name":"DEPARTMENT OF MATHEMATICS ETH, 8092 ZURICH SWITZERLAND"},{"name":"DEPARTMENT OF MATHEMATICS UCLA, LOS ANGELES CA 90095"}]}],"member":"311","published-online":{"date-parts":[[2013,8,23]]},"reference":[{"key":"e_1_2_7_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(86)90214-1"},{"key":"e_1_2_7_3_1","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190180610"},{"key":"e_1_2_7_4_1","first-page":"34","article-title":"A problem of Erd\u0151s on the minimum of k\u2010cliques","volume":"103","author":"Das S.","year":"2013","journal-title":"J Combin Theory Ser"},{"key":"e_1_2_7_5_1","unstructured":"P.Erd\u0151s D. 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L.Rothschild Asymptotic enumeration of\u2010free graphs Theorie Combinatorie Proceedings of the Conference Vol. II Rome 1973 Roma Acad Nazionale dei Lincei 1976 pp.19\u201327."},{"key":"e_1_2_7_6_1","first-page":"459","article-title":"On the number of complete subgraphs contained in certain graphs","volume":"7","author":"Erd\u0151s P.","year":"1962","journal-title":"Magyar Tud Akad Mat Kutat\u00f3 Int K\u00f6zl"},{"key":"e_1_2_7_7_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1946-08715-7"},{"key":"e_1_2_7_8_1","first-page":"5","article-title":"Dense packings of induced subgraphs","volume":"22","author":"Exoo G.","year":"1986","journal-title":"Ars Combin"},{"key":"e_1_2_7_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(93)90366-2"},{"key":"e_1_2_7_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(79)90016-9"},{"key":"e_1_2_7_11_1","doi-asserted-by":"publisher","DOI":"10.2307\/2310464"},{"key":"e_1_2_7_12_1","unstructured":"H.Hatami J.Hirst andS.Norine The inducibility of blow\u2010up graphs arXiv preprint arXiv:1108.5699 2011."},{"key":"e_1_2_7_13_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-2010-00687-X"},{"key":"e_1_2_7_14_1","unstructured":"J.Hirst The inducibility of graphs on four vertices arXiv preprint arXiv:1109.1592 2011."},{"key":"e_1_2_7_15_1","unstructured":"H.Huang N.Linial H.Naves Y.Peled andB.Sudakov On the densities of cliques and independent sets in graphs(submitted)."},{"key":"e_1_2_7_16_1","first-page":"187","volume-title":"A Theorem of Finite Sets","author":"Katona G.","year":"1968"},{"key":"e_1_2_7_17_1","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1525\/9780520319875-014","volume-title":"The Number of Simplices in a Complex, Mathematical Optimization Techniques","author":"Kruskal J.","year":"1963"},{"key":"e_1_2_7_18_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-2010-05189-X"},{"key":"e_1_2_7_19_1","unstructured":"O.Pikhurko Minimum number ofk\u2010cliques in graphs with bounded independence number(submitted)."},{"key":"e_1_2_7_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(75)90084-2"},{"key":"e_1_2_7_21_1","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1203350785"},{"key":"e_1_2_7_22_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548308009085"},{"key":"e_1_2_7_23_1","doi-asserted-by":"publisher","DOI":"10.1137\/090747476"},{"key":"e_1_2_7_24_1","unstructured":"C.Reiher Minimizing the number of cliques in graphs of given order and edge density manuscript."},{"key":"e_1_2_7_25_1","unstructured":"K.Sperfeld On the minimal monochromaticK4\u2010density arXiv preprint arXiv:1106.1030 2011."},{"key":"e_1_2_7_26_1","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s2-39.2.246"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.21762","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.21762","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,3]],"date-time":"2023-10-03T19:59:35Z","timestamp":1696363175000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.21762"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,8,23]]},"references-count":25,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2014,7]]}},"alternative-id":["10.1002\/jgt.21762"],"URL":"https:\/\/doi.org\/10.1002\/jgt.21762","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,8,23]]}}}