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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 852.52009

**Autor: ** Erdös, Paul; Purdy, George

**Title: ** Extremal problems in combinatorial geometry. (In English)

**Source: ** Graham, R. L. (ed.) et al., Handbook of combinatorics. Vol. 1-2. Amsterdam: Elsevier (North-Holland), 809-874 (1995).

**Review: ** This interesting paper gives an overview about extremal problems on combinatorial geometry.

Among others the following topics are discussed: Sylvester-Gallai theorems, The Motzkin-Dirac conjecture on the number of Gallai lines. Arrangements, the Graham-Newman problem, the orchard problem, Diracs problem, allowable n-sequences of Goodman and Pollack, Metric problems (Borsuks problem, the Hadwiger-Nelson problem, triangles of different areas, problems involving circles), Helly-type theorems and selected topics (Euclidean Ramsey problems, Heilbronn's problem and other problems).

Several interesting conjectures and many references are included.

**Reviewer: ** H.-D.Hecker (Jena)

**Classif.: ** * 52C10 Erdoes problems and related topics of discrete geometry

00A07 Problem books

**Keywords: ** extremal problems; combinatorial geometry

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