{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,19]],"date-time":"2026-06-19T17:42:27Z","timestamp":1781890947133,"version":"3.54.5"},"reference-count":24,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2016,9,20]],"date-time":"2016-09-20T00:00:00Z","timestamp":1474329600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/http\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["GRK 1408"],"award-info":[{"award-number":["GRK 1408"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[2017,6]]},"abstract":"Abstract<\/jats:title>Let F<\/jats:italic> be a graph that contains an edge whose deletion reduces its chromatic number. For such a graph F<\/jats:italic>, a classical result of Simonovits from 1966 shows that every graph on vertices with more than edges contains a copy of F<\/jats:italic>. In this article we derive a similar theorem for multipartite graphs. For a graph H<\/jats:italic> and an integer , let be the minimum real number such that every \u2113\u2010partite graph whose edge density between any two parts is greater than contains a copy of H<\/jats:italic>. Our main contribution in this article is to show that for all sufficiently large if and only if H<\/jats:italic> admits a vertex\u2010coloring with colors such that all color classes but one are independent sets, and the exceptional class induces just a matching. When H<\/jats:italic> is a complete graph, this recovers a result of Pfender (Combinatorica 32 (2012), 483\u2013495). We also consider several extensions of Pfender's result.<\/jats:p>","DOI":"10.1002\/jgt.22075","type":"journal-article","created":{"date-parts":[[2016,9,20]],"date-time":"2016-09-20T08:04:45Z","timestamp":1474358685000},"page":"496-524","source":"Crossref","is-referenced-by-count":1,"title":["A Density Tur\u00e1n Theorem"],"prefix":"10.1002","volume":"85","author":[{"given":"Lothar","family":"Narins","sequence":"first","affiliation":[{"name":"INSTITUTE OF COMPUTER SCIENCE CZECH ACADEMY OF SCIENCES PRAGUE CZECH REPUBLIC"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tuan","family":"Tran","sequence":"additional","affiliation":[{"name":"INSTITUTE OF COMPUTER SCIENCE CZECH ACADEMY OF SCIENCES PRAGUE CZECH REPUBLIC"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2016,9,20]]},"reference":[{"key":"e_1_2_8_2_1","volume-title":"Extremal Graph Theory","author":"Bollob\u00e1s B.","year":"1978"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(75)90011-4"},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2007.03.045"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-006-0009-y"},{"key":"e_1_2_8_6_1","unstructured":"C.Edwards A lower bound for the largest number of triangles with a common edge Unpublished manuscript 1977."},{"key":"e_1_2_8_7_1","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1215\/ijm\/1255631811","article-title":"On a theorem of Rademacher\u2013Tur\u00e1n","volume":"6","author":"Erd\u0151s P.","year":"1962","journal-title":"Illinois J Math"},{"key":"e_1_2_8_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02759702"},{"key":"e_1_2_8_9_1","first-page":"117","volume-title":"Theory of Graphs (International Symposium, Rome, 1966)","author":"Erd\u0151s P.","year":"1967"},{"key":"e_1_2_8_10_1","doi-asserted-by":"publisher","DOI":"10.21136\/CPM.1969.108598"},{"key":"e_1_2_8_11_1","first-page":"51","article-title":"A limit theorem in graph theory","volume":"1","author":"Erd\u0151s P.","year":"1966","journal-title":"Studia Sci Math Hung"},{"key":"e_1_2_8_12_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579235"},{"key":"e_1_2_8_13_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1946-08715-7"},{"key":"e_1_2_8_14_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548305007157"},{"key":"e_1_2_8_15_1","first-page":"1315","article-title":"Solution of a problem of P. Erd\u0151s about the maximum number of triangles with a common edge in a graph","volume":"32","author":"Khad\u017eiivanov N.","year":"1979","journal-title":"C R Acad Bulg Sci"},{"key":"e_1_2_8_16_1","first-page":"60","article-title":"Problem 28","volume":"10","author":"Mantel W.","year":"1907","journal-title":"Wiskundige Opgaven"},{"key":"e_1_2_8_17_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.37236\/533","article-title":"A multipartite version of the Tur\u00e1n problem\u2014Density conditions and eigenvalues","volume":"18","author":"Nagy Z.","year":"2011","journal-title":"Electron J Combin"},{"key":"e_1_2_8_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2009.08.004"},{"key":"e_1_2_8_19_1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139004114.005"},{"key":"e_1_2_8_20_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-012-2425-5"},{"key":"e_1_2_8_21_1","unstructured":"F.Pfender Personal communication."},{"key":"e_1_2_8_22_1","unstructured":"I.RuzsaandE.Szemer\u00e9di Triple systems with no six points carrying three triangles Combinatorics Proceedings of the Fifth Hungarian Colloq. Keszthely 1976."},{"key":"e_1_2_8_23_1","unstructured":"M.Simonovits A method for solving extremal problems in graph theory Theory of Graphs Proc. Coll. Tihany 1966 pp.279\u2013319."},{"key":"e_1_2_8_24_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-006-0019-9"},{"key":"e_1_2_8_25_1","first-page":"436","article-title":"On an extremal problem in graph theory","volume":"48","author":"Tur\u00e1n P.","year":"1941","journal-title":"Mat Fiz Lapok"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.22075","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.22075","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.22075","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,6]],"date-time":"2023-10-06T03:40:24Z","timestamp":1696563624000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.22075"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,9,20]]},"references-count":24,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2017,6]]}},"alternative-id":["10.1002\/jgt.22075"],"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1002\/jgt.22075","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,9,20]]}}}