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Turán's theorem
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==References== {{reflist|refs= <ref name=az>{{citation | last1 = Aigner | first1 = Martin | author1-link = Martin Aigner | last2 = Ziegler | first2 = Günter M. | author2-link = Günter M. Ziegler | contribution = Chapter 41: Turán’s graph theorem | doi = 10.1007/978-3-662-57265-8_41 | edition = 6th | isbn = 978-3-662-57265-8 | pages = 285–289 | publisher = Springer-Verlag | title = Proofs from THE BOOK | title-link = Proofs from THE BOOK | year = 2018}}</ref> <ref name=bondy>{{citation | last = Bondy | first = J. A. | authorlink = John Adrian Bondy | doi = 10.1016/0095-8956(71)90016-5 | issue = 1 | journal = Journal of Combinatorial Theory, Series B | pages = 80–84 | title = Pancyclic graphs I | volume = 11 | year = 1971| doi-access = }}</ref> <ref name=erdos>{{citation | last = Erdős | first = Pál | authorlink = Paul Erdős | journal = Matematikai Lapok | language = Hungarian | mr = 307975 | pages = 249–251 | title = Turán Pál gráf tételéről | trans-title = On the graph theorem of Turán | url = https://users.renyi.hu/~p_erdos/1971-27.pdf | volume = 21 | year = 1970}}</ref> <ref name=egp>{{citation | last1 = Erdős | first1 = Paul | authorlink1 = Paul Erdős | last2 = Goodman | first2 = A. W. | authorlink2 = Adolph Winkler Goodman | last3 = Pósa | first3 = Louis | authorlink3 = Lajos Pósa (mathematician) | title = The representation of a graph by set intersections | url = http://www.renyi.hu/~p_erdos/1966-21.pdf | journal = Canadian Journal of Mathematics | volume = 18 | issue = 1 | year = 1966 | pages = 106–112 | mr = 0186575 | doi = 10.4153/CJM-1966-014-3 | s2cid = 646660 | access-date = 2011-03-05 | archive-date = 2021-04-16 | archive-url = https://web.archive.org/web/20210416163126/https://www.renyi.hu/~p_erdos/1966-21.pdf | url-status = live }}</ref> <ref name=mantel>{{citation | last = Mantel | first = W. | journal = Wiskundige Opgaven | pages = 60–61 | title = Problem 28 (Solution by H. Gouwentak, W. Mantel, J. Teixeira de Mattes, F. Schuh and W. A. Wythoff) | volume = 10 | year = 1907}}</ref> <ref name=ms>{{citation | last1 = Motzkin | first1 = T. S. | author1-link = Theodore Motzkin | last2 = Straus | first2 = E. G. | author2-link = Ernst G. Straus | doi = 10.4153/CJM-1965-053-6 | journal = [[Canadian Journal of Mathematics]] | mr = 175813 | pages = 533–540 | title = Maxima for graphs and a new proof of a theorem of Turán | volume = 17 | year = 1965| s2cid = 121387797 | doi-access = free }}</ref> <ref name=turan>{{Citation | last = Turán | first = Paul | authorlink = Pál Turán | year = 1941 | title = On an extremal problem in graph theory | journal = Matematikai és Fizikai Lapok | volume = 48 | pages = 436–452 | language = Hungarian}}</ref> <ref name=zykov>{{Citation | last = Zykov | first = A. | year = 1949 | title = On some properties of linear complexes | journal = Mat. Sb. |series=New Series | volume = 24 | pages = 163–188 | language = Russian}}</ref> <ref name=alonshik>{{citation | last1 = Alon | first1 = Noga | last2 = Shikhelman | first2 = Clara | doi = 10.1016/j.jctb.2016.03.004 | journal = Journal of Combinatorial Theory, Series B | pages = 146–172 | title = Many T copies in H-free graphs | volume = 121 | year = 2016| s2cid = 5552776 | doi-access = free | arxiv = 1409.4192 }}</ref> <ref name=raz>{{Cite journal|last=Razborov|first=Alexander|date=2008|title=On the minimal density of triangles in graphs.|url=http://people.cs.uchicago.edu/~razborov/files/triangles.pdf|journal=Combinatorics, Probability and Computing|volume=17|issue=4|pages=603–618|doi=10.1017/S0963548308009085|s2cid=26524353|via=MathSciNet (AMS)|archive-date=2021-11-30|access-date=2021-11-28|archive-url=https://web.archive.org/web/20211130062334/http://people.cs.uchicago.edu/~razborov/files/triangles.pdf|url-status=live}}</ref> <ref name=reiher>{{citation | last = Reiher | first = Christian | doi = 10.4007/annals.2016.184.3.1 | journal = Annals of Mathematics | pages = 683–707 | title = The clique density theorem | volume = 184 | year = 2016| issue = 3 | arxiv = 1212.2454 | s2cid = 59321123 }}</ref> <ref name=largenetworks>{{citation | last = Lovász | first = László | title = Large networks and graph limits}}</ref> }} {{DEFAULTSORT:Turans theorem}} [[Category:Extremal graph theory]] [[Category:Theorems in graph theory]] [[Category:Articles containing proofs]]
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