Ramsey theory. 2nd ed. (English) Zbl 0705.05061

Graham, Ronald L.; Rothschild, Bruce L.; Spencer, Joel H.

Wiley-Interscience Series in Discrete Mathematics and Optimization. New York etc.: John Wiley & Sons. xi, 196 p. $ 39.30 (1990).

[For a review of the first ed. (1980), cf. Zbl 0455.05002.]
In the second edition of this beautiful book, the bulk of the text remains unchanged. We find the following additions.
1. Shelah’s brilliant elementary proof of the Hales-Jewett theorem which implies van der Waerden’s theorem and much lower growth rates of some of the upper bounds involved.
2. An updated table 4.1 of values and bounds for R(m,n) which is the minimal k so that any graph on k vertices contains either a clique of size m or an independent set of size n.
3. A different graph in Figure 4.1 (b). 4. Theorem 4 on p. 123 which gives an induced and restricted vector space version of Ramsey’s Theorem.
5. New information about Euclidean Ramsey configurations on p. 137.
6. 11 new references added and 2 old ones deleted.
Although some typographical errors have been corrected, there are quite a few still left unnoticed.

Reviewer: Ko-Wei Li

MSC:

05D10	Ramsey theory
05-02	Research exposition (monographs, survey articles) pertaining to combinatorics

Keywords:

Ramsey theory

Citations:

Zbl 0455.05002