Abstract
We prove a new upper bound for diagonal two-colour Ramsey numbers, showing that there exists a constant $C$ such that \[r(k+1, k+1) \leq k^{- C {\log k}/{\log \log k}} \textstyle \binom{2k}{k}.\]
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TITLE = {Quasi-random graphs},
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FJOURNAL = {Combinatorica. An International Journal on Combinatorics and the Theory of Computing},
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MRREVIEWER = {Zbigniew Palka},
} -
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AUTHOR = {Erdős, P. and Szekeres, G.},
TITLE = {A combinatorial problem in geometry},
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ZBLNUMBER = {0012.27010},
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TITLE = {Numbers in {R}amsey theory},
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VENUE = {New Cross, 1987},
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ZBLNUMBER = {0633.05049},
MRREVIEWER = {Walter A. Deuber},
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EDITOR = {Karo{ń}ski, Micha{\l}and Palka, Zbigniew},
TITLE = {Pseudorandom graphs},
BOOKTITLE = {Random Graphs {\rm'85}},
VENUE = {Poznań, Poland, 1985},
SERIES = {North-Holland Math. Stud.},
NUMBER = {144},
PAGES = {307--331},
PUBLISHER = {North-Holland},
ADDRESS = {Amsterdam},
YEAR = {1987},
MRCLASS = {05C80},
MRNUMBER = {89d:05158},
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ZBLNUMBER = {0632.05045},
} -
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AUTHOR = {Thomason, Andrew},
TITLE = {An upper bound for some {R}amsey numbers},
JOURNAL = {J. Graph Theory},
FJOURNAL = {Journal of Graph Theory},
VOLUME = {12},
YEAR = {1988},
NUMBER = {4},
PAGES = {509--517},
ISSN = {0364-9024},
CODEN = {JGTHDO},
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