Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  308.05001
Autor:  Erdös, Paul; Spencer, Joel
Title:  Probabilistic methods in combinatorics. (In English)
Source:  Budapest: Akademiai Kiado. 106 p. Ft 70.00 (1974).
Review:  One way to show the existence of an object with a property P is by construction. Another way is to show that the probability that objects in some set have property P is positive. For example, if the expected value of some integer-valued parameter f(x) is less than one, then it follows that there exists an object x for which f(x) = 0. The purely probabilistic aspects of such arguments are often fairly simple; but obtaining estimates for the probabilities involved may or may not be so simple. This ``probabilistic method'' is important because in many different problems it has yielded results that are as good or better than have been obtained by other methods. This monograph is a collection of such applications to, among other things, sets with property B, subtournaments of a tournament, the chromatic number of a graph, asyummetric graphs, random graphs, Zarankiewicz's problem, and problems related to theorems of Ramsey, van der Waerden, and Turán.
Reviewer:  J.W.Moon
Classif.:  * 05-XX Combinatorics
                   60C05 Combinatorial probability
                   05A99 Classical combinatorial problems
                   05Cxx Graph theory
                   05-02 Research monographs (combinatorics)

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Books Problems Set Theory Combinatorics Extremal Probl/Ramsey Th.
Graph Theory Add.Number Theory Mult.Number Theory Analysis Geometry
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