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» Upper and lower Ramsey bounds in bounded arithmetic
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DM
2007
89views more  DM 2007»
13 years 6 months ago
New upper bound formulas with parameters for Ramsey numbers
In this paper, we obtain some new results R(5, 12) 848, R(5, 14) 1461, etc., and we obtain new upper bound formulas for Ramsey numbers with parameters. © 2006 Published by Elsevi...
Yi Ru Huang, Yuandi Wang, Wancheng Sheng, Jian She...
ENDM
2007
96views more  ENDM 2007»
13 years 6 months ago
Sub-Ramsey Numbers for Arithmetic Progressions and Schur Triples
For a given positive integer k, sr(m, k) denotes the minimal positive integer such that every coloring of [n], n ≥ sr(m, k), that uses each color at most k times, yields a rainb...
Jacob Fox, Veselin Jungic, Rados Radoicic
COMBINATORICS
2000
87views more  COMBINATORICS 2000»
13 years 6 months ago
Symmetric Sum-Free Partitions and Lower Bounds for Schur Numbers
We give new lower bounds for the Schur numbers S(6) and S(7). This will imply new lower bounds for the Multicolor Ramsey Numbers R6(3) and R7(3). We also make several observations...
Harold Fredricksen, Melvin M. Sweet
JGT
2008
92views more  JGT 2008»
13 years 6 months ago
A new upper bound for the bipartite Ramsey problem
We consider the following question: how large does n have to be to guarantee that in any two-colouring of the edges of the complete graph Kn,n there is a monochromatic Kk,k? In th...
David Conlon