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Ramsey's theorem
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== References == *{{citation | last1 = Ajtai | first1 = Miklós | author1-link = Miklós Ajtai | last2 = Komlós | first2 = János | author2-link = János Komlós (mathematician) | last3 = Szemerédi | first3 = Endre | author3-link = Endre Szemerédi | journal = J. Combin. Theory Ser. A | pages = 354–360 | title = A note on Ramsey numbers | volume = 29 | year = 1980 | doi = 10.1016/0097-3165(80)90030-8 | issue = 3| doi-access = free }}. *{{citation | last1 = Bohman | first1 = Tom | last2 = Keevash | first2 = Peter | journal = Invent. Math. | pages = 291–336 | title = The early evolution of the H-free process | volume = 181 | year = 2010 | doi = 10.1007/s00222-010-0247-x | issue = 2| arxiv = 0908.0429| bibcode = 2010InMat.181..291B| s2cid = 2429894 }} *{{citation|first=Richard A.|last=Brualdi|title=Introductory Combinatorics|edition=5th|year=2010|publisher=Prentice-Hall|isbn=978-0-13-602040-0|pages=77–82}} *{{citation | last = Conlon | first = David | journal = [[Annals of Mathematics]] | pages = 941–960 | title = A new upper bound for diagonal Ramsey numbers | volume = 170 | year = 2009 | doi = 10.4007/annals.2009.170.941 | issue = 2 | mr = 2552114| arxiv = math/0607788v1 | s2cid = 9238219 }}. *{{citation | last = Erdős | first = Paul | author-link = Paul Erdős | journal = Bull. Amer. Math. Soc. | pages = 292–294 | title = Some remarks on the theory of graphs | volume = 53 | year = 1947 | doi = 10.1090/S0002-9904-1947-08785-1 | issue = 4| doi-access = free }}. *{{citation | last1 = Erdős | first1 = P. | author1-link = Paul Erdős | last2 = Moser | first2 = L. | journal = A Magyar Tudományos Akadémia, Matematikai Kutató Intézetének Közleményei | mr = 168494 | pages = 125–132 | title = On the representation of directed graphs as unions of orderings | url = https://users.renyi.hu/~p_erdos/1964-22.pdf | volume = 9 | year = 1964}} *{{citation | last1 = Erdős | first1 = Paul | author1-link = Paul Erdős | last2 = Szekeres | first2 = George | author2-link = George Szekeres | journal = [[Compositio Mathematica]] | pages = 463–470 | title = A combinatorial problem in geometry | volume = 2 | year = 1935 | doi = 10.1007/978-0-8176-4842-8_3 | isbn = 978-0-8176-4841-1| url = http://www.numdam.org/article/CM_1935__2__463_0.pdf }}. *{{citation | last = Exoo | first = G. | journal = Journal of Graph Theory | pages = 97–98 | title = A lower bound for R(5,5) | volume = 13 | year = 1989 | doi = 10.1002/jgt.3190130113}}. *{{citation | last1 = Graham | first1 = R. | author1-link = Ronald Graham | last2 = Rothschild | first2 = B. | last3 = Spencer | first3 = J. H. | author3-link = Joel Spencer | location = New York | publisher = John Wiley and Sons | title = Ramsey Theory | journal = Scientific American | year = 1990| volume = 263 | issue = 1 | page = 112 | doi = 10.1038/scientificamerican0790-112 | bibcode = 1990SciAm.263a.112G }}. *{{citation|first=Jonathan L.|last=Gross|title=Combinatorial Methods with Computer Applications|year=2008|publisher=CRC Press|isbn=978-1-58488-743-0|page=458}} *{{citation|first=Frank|last=Harary|title=Graph Theory|year=1972|publisher=Addison-Wesley|isbn=0-201-02787-9|pages=16–17}} *{{citation | doi =10.1112/plms/s2-30.1.264 | last = Ramsey | first = F. P. | author-link = Frank P. Ramsey | journal = Proceedings of the London Mathematical Society | pages = 264–286 | title = On a problem of formal logic | volume = 30 | year = 1930}}. *{{citation | last = Spencer | first = J. |author-link = Joel H. Spencer | journal = J. Combin. Theory Ser. A | pages = 108–115 | title = Ramsey's theorem – a new lower bound | volume = 18 | year = 1975 | doi = 10.1016/0097-3165(75)90071-0| doi-access = free }}. *{{citation | last1 = Bian | first1 = Zhengbing | last2 = Chudak | first2 = Fabian | last3 = Macready | first3 = William G. | last4 = Clark | first4 = Lane | last5 = Gaitan | first5 = Frank | title = Experimental determination of Ramsey numbers | journal = Physical Review Letters | volume = 111 | issue = 13 | pages = 130505 | year = 2013 | doi = 10.1103/PhysRevLett.111.130505 | bibcode=2013PhRvL.111m0505B | pmid=24116761| arxiv = 1201.1842| s2cid = 1303361 }}.
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