Problems and results on graphs and hypergraphs: Similarities and differences. (English) Zbl 0725.05051

Erdős, Paul

Mathematics of Ramsey theory, Coll. Pap. Symp. Graph Theory, Prague/Czech., Algorithms Comb. 5, 12-28 (1990).

[For the entire collection see Zbl 0715.00011.]
Many papers and also the excellent book of B. Bollobas [Extremal graph theory (1978; Zbl 0419.05031)] discussed the extremal problems on graphs. But much fewer papers have appeared on extremal problems on hypergraphs. In this survey, which is written in the classical Erdős style, the author discusses and suggests many selected extremal problems on graphs and hypergraphs. He tries to emphasize the new difficulties arising in the study of hypergraphs. In the five chapters of this paper the author deals successively with classical extremal problems of Turan type, density problems, Ramsey’s theorem, Ramsey-Turan type problems, and problems about chromatic numbers of graphs and hypergraphs. The paper is very interesting and challenging, especially to hypergraph researchers.

Reviewer: Kan Jiahai (Nanjing)

MSC:

05C35	Extremal problems in graph theory
05-02	Research exposition (monographs, survey articles) pertaining to combinatorics
00A07	Problem books
05C65	Hypergraphs
05D10	Ramsey theory
05C55	Generalized Ramsey theory

Keywords:

extremal problems on graphs; extremal problems on hypergraphs; survey; density problems; Ramsey’s theorem; Ramsey-Turan type problems; chromatic numbers