## Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  423.05001
Autor:  Erdös, Paul
Title:  Problems and results in combinatorial analysis and combinatorial number theory. (In English)
Source:  Proc. 9th southeast. Conf. on Combinatorics, graph theory, and computing, Boca Raton 1978, 29-40 (1978).
Review:  [For the entire collection see Zbl 396.00003.]
There are six sections: 1. Conjecture of Faber, Lovász and myself (concerning colouring problems for set systems). 2. Some old extremal problems (''Turán-type'' problems for undirected graphs). 3. some problems on probabilistic graph theory. 4. Further problems (''which arose in our work with Faudree, Rousseau and Schelp'' concerning generalized Ramsey theory). 5. Erdös-Rado Conjecture on \triangle-systems (that there exists a constant C such that Cn exceeds the maximum number of n-element sets, no three having pairwise the same intersection). 6. Work with Ulam and Selfridge containing the following theorems: ''Theorem 1 (with Selfridge): Let u = k2-1. To every \epsilon > 0 there is a sequence of primes p0 < ... < pu and an interval I of length (3-\epsilon)pu, which contains exactly 2k distinct multiples of the p's.'' ''Theorem 2(with Ulam): Let |S| = n. There is a division of the subsets of S into two classes so that if ai\subseteq S, s \leq i \leq k are such that all the 2k-1 unions Ai1... Air are distinct and belong to the same class then k \leq (1+0(1))\frac{log n}{log 2}.''
Reviewer:  W.G.Brown
Classif.:  * 05-02 Research monographs (combinatorics)
05C55 Generalized Ramsey theory
05C35 Extremal problems (graph theory)
05C65 Hypergraphs
11N05 Distribution of primes
05C15 Chromatic theory of graphs and maps
05A05 Combinatorial choice problems
05A99 Classical combinatorial problems
11B39 Special numbers, etc.
00A07 Problem books
Keywords:  delta systems; colouring problems; set systems; extremal problems; probabilistic graph theory; generalized Ramsey theory; Erdös-Rado conjecture
Index Words:  Problems
Citations:  Zbl.396.00003

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