| N. Alon and P. Pudlak, Constructive Lower Bounds for off-diagonal Ramsey Numbers, Israel Journal of Mathematics, 122 (2001) 243-251. |
.... obtained a breakthrough by proving that R (3, k ) has order of magnitude exactly Q(k 2 log k ) Good asymptotic bounds for R (k , k ) can be found, for example, in [Chu3, McS] lower bound) and [Tho] upper bound) and for many other asymptotic bounds in the general case of R (k , l ) consult [GRS, GrRo , AP]. 5 THE ELECTRONIC JOURNAL OF COMBINATORICS (2001) DS1.8 All the lower bounds for higher numbers listed in Table II were obtained by construction of cyclic graphs. l 15 16 17 18 19 20 21 22 23 k 73 79 92 98 106 109 122 125 136 3 WW WW WWY1 WWY1 WWY1 WWY1 WWY1 WWY1 WWY1 145 164 182 198 230 ....
....Other general results: Wa1] R (k , k ) 4R (k , k 2) 2. Chv] R (K n , T m ) n 1) m 1) 1 for any tree T on m vertices. CH2] R (G , H ) c(G ) 1) c (H ) 1) 1, where c(G ) is the chromatic number of G , and c (H ) is the size of the largest connected component of H . [AP] Constructive asymptotic lower bounds for R (k , l ) BE1] R (G ,G ) 4n (G ) 1) 3 for any connected G . BE2] Graphs yielding R (K n , G ) n 1) n (G ) 1) 1 and related results (see also [EFRS5] BES] Study of Ramsey numbers for multiple copies of graphs. See also [Bu1, LorMu] ....
N. Alon and P. Pudlak, Constructive Lower Bounds for off-diagonal Ramsey Numbers, Israel Journal of Mathematics, 122 (2001) 243-251.
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N. Alon and P. Pudlak, Constructive Lower Bounds for off-diagonal Ramsey Numbers, Israel Journal of Mathematics, 122 (2001) 243-251.
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