{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,22]],"date-time":"2025-04-22T05:03:38Z","timestamp":1745298218225},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,11,24]],"date-time":"2021-11-24T00:00:00Z","timestamp":1637712000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,11,24]],"date-time":"2021-11-24T00:00:00Z","timestamp":1637712000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Combinatorica"],"published-print":{"date-parts":[[2022,2]]},"DOI":"10.1007\/s00493-021-4340-0","type":"journal-article","created":{"date-parts":[[2021,11,23]],"date-time":"2021-11-23T22:02:49Z","timestamp":1637704969000},"page":"115-136","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["On the Ramsey-Tur\u00e1n Density of Triangles"],"prefix":"10.1007","volume":"42","author":[{"given":"Tomasz","family":"\u0141uczak","sequence":"first","affiliation":[]},{"given":"Joanna","family":"Polcyn","sequence":"additional","affiliation":[]},{"given":"Christian","family":"Reiher","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,11,24]]},"reference":[{"key":"4340_CR1","doi-asserted-by":"publisher","first-page":"443","DOI":"10.1007\/BF02020809","volume":"13","author":"B Andr\u00e1sfai","year":"1962","unstructured":"B. Andr\u00e1sfai: \u00dcber ein Extremalproblem der Graphentheorie, Acta Math. Acad. Sci. Hungar. 13 (1962), 443\u2013455.","journal-title":"Acta Math. Acad. Sci. Hungar."},{"key":"4340_CR2","doi-asserted-by":"publisher","first-page":"166","DOI":"10.1016\/0095-8956(76)90057-5","volume":"21","author":"B Bollob\u00e1s","year":"1976","unstructured":"B. Bollob\u00e1s and P. Erd\u0151s: On a Ramsey-Tur\u00e1n type problem, J. Combinatorial Theory Ser. B 21 (1976), 166\u2013168.","journal-title":"J. Combinatorial Theory Ser. B"},{"key":"4340_CR3","doi-asserted-by":"publisher","first-page":"662","DOI":"10.1016\/j.disc.2009.05.021","volume":"310","author":"S Brandt","year":"2010","unstructured":"S. Brandt: Triangle-free graphs whose independence number equals the degree, Discrete Math. 310 (2010), 662\u2013669.","journal-title":"Discrete Math."},{"key":"4340_CR4","doi-asserted-by":"publisher","first-page":"#R43","DOI":"10.37236\/1381","volume":"5","author":"S Brandt","year":"1998","unstructured":"S. Brandt and T. Pisanski:. Another infinite sequence of dense triangle-free graphs. Electron. J. Combin. 5 (1998), #R43.","journal-title":"Electron. J. Combin."},{"key":"4340_CR5","unstructured":"S. Brandt and S. Thomass\u00e9: Dense triangle-free graphs are four-colorable: A solution to the Erd\u0151s-Simonovits problem, available from Thomass\u00e9\u2019s webpage at http:\/\/perso.ens-lyon.fr\/stephan.thomasse\/."},{"key":"4340_CR6","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1007\/BF02579342","volume":"3","author":"P Erd\u0151s","year":"1983","unstructured":"P. Erd\u0151s, A. Hajnal, V. T. S\u00f3s and E. Szemer\u00e9di: More results on Ramsey-Turaan type problems, Combinatorica 3 (1983), 69\u201381.","journal-title":"Combinatorica"},{"key":"4340_CR7","first-page":"51","volume":"1","author":"P Erd\u0151s","year":"1966","unstructured":"P. Erd\u0151s and M. Simonovits: A limit theorem in graph theory, Studia Sci. Math. Hungar. 1 (1966), 51\u201357.","journal-title":"Studia Sci. Math. Hungar."},{"key":"4340_CR8","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1016\/0012-365X(73)90126-X","volume":"5","author":"P Erd\u0151s","year":"1973","unstructured":"P. Erd\u0151s and M. Simonovits: On a valence problem in extremal graph theory, Discrete Math. 5 (1973), 323\u2013334.","journal-title":"Discrete Math."},{"key":"4340_CR9","unstructured":"P. Erd\u0151s and V. T. S\u00f3s: Some remarks on Ramsey\u2019s and Tur\u00e1n\u2019s theorem, in: Colloquia mathematica societatis J\u00e1nos Bolyai, 4. Combinatorial theory and its applications, Balatonf\u00fcred (Hungary), 1969, 395\u2013404, 1970."},{"key":"4340_CR10","doi-asserted-by":"publisher","first-page":"1087","DOI":"10.1090\/S0002-9904-1946-08715-7","volume":"52","author":"P Erd\u0151s","year":"1946","unstructured":"P. Erd\u0151s and A. H. Stone: On the structure of linear graphs, Bull. Amer. Math. Soc. 52 (1946), 1087\u20131091.","journal-title":"Bull. Amer. Math. Soc."},{"key":"4340_CR11","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1112\/jlms\/s1-10.37.26","volume":"10","author":"Ph Hall","year":"1935","unstructured":"Ph. Hall: On representatives of subsets, Journal of the London Mathematical Society 10 (1935), 26\u201330.","journal-title":"Journal of the London Mathematical Society"},{"key":"4340_CR12","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1002\/jgt.22682","volume":"98","author":"T \u0141uczak","year":"2021","unstructured":"T. \u0141uczak, J. Polcyn and Chr. Reiher: Andr\u00e1sfai and Vega graphs in Ramsey-Tur\u00e1n theory, Journal of Graph Theory 98 (2021), 57\u201380.","journal-title":"Journal of Graph Theory"},{"key":"4340_CR13","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1007\/s00493-006-0028-8","volume":"26","author":"T \u0141uczak","year":"2006","unstructured":"T. \u0141uczak: On the structure of triangle-free graphs of large minimum degree, Combinatorica 26 (2006), 489\u2013493.","journal-title":"Combinatorica"},{"key":"4340_CR14","doi-asserted-by":"publisher","first-page":"613","DOI":"10.1007\/s11856-019-1831-4","volume":"230","author":"C M L\u00fcders","year":"2019","unstructured":"C. M. L\u00fcders and Chr. Reiher: The Ramsey-Tur\u00e1n problem for cliques, Israel J. Math. 230 (2019), 613\u2013652.","journal-title":"Israel J. Math."},{"key":"4340_CR15","first-page":"60","volume":"10","author":"W Mantel","year":"1907","unstructured":"W. Mantel: Problem 28 (solution by H. Gouwentak, W. Mantel, J. Teixeira de Mattes, F. Schuh and W. A. Wythoff), Wiskundige Opgaven 10 (1907), 60\u201361.","journal-title":"Wiskundige Opgaven"},{"key":"4340_CR16","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1016\/S0012-365X(00)00214-4","volume":"229","author":"M Simonovits","year":"2001","unstructured":"M. Simonovits and V. T. S\u00f3s: Ramsey-Tur\u00e1n theory, Discrete Math. 229 (2001), 293\u2013340.","journal-title":"Discrete Math."},{"key":"4340_CR17","first-page":"113","volume":"23","author":"E Szemer\u00e9di","year":"1973","unstructured":"E. Szemer\u00e9di:. On graphs containing no complete subgraph with 4 vertices. Mat. Lapok 23 (1972), 113\u2013116 (1973).","journal-title":"Mat. Lapok"},{"key":"4340_CR18","unstructured":"P. Tur\u00e1n: On an extremal problem in graph theory, Matematikai \u00e9s Fizikai Lapok (in Hungarian) (1948), 436\u2013452."},{"key":"4340_CR19","first-page":"163","volume":"24","author":"A A Zykov","year":"1949","unstructured":"A. A. Zykov: On some properties of linear complexes, Mat. Sbornik N.S. 24 (1949), 163\u2013188.","journal-title":"Mat. Sbornik N.S."}],"container-title":["Combinatorica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-021-4340-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00493-021-4340-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-021-4340-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,23]],"date-time":"2022-05-23T18:07:36Z","timestamp":1653329256000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00493-021-4340-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,24]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,2]]}},"alternative-id":["4340"],"URL":"https:\/\/doi.org\/10.1007\/s00493-021-4340-0","relation":{},"ISSN":["0209-9683","1439-6912"],"issn-type":[{"value":"0209-9683","type":"print"},{"value":"1439-6912","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,24]]},"assertion":[{"value":"16 October 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 November 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 November 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}