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Extremal problems in combinatorial geometry. (English) Zbl 0852.52009
Graham, R. L. (ed.) et al., Handbook of combinatorics. Vol. 1-2. Amsterdam: Elsevier (North-Holland), 809-874 (1995).
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.
For the entire collection see [Zbl 0833.05001].
Reviewer: H.-D.Hecker (Jena)

MSC:
52C10 Erdős problems and related topics of discrete geometry
00A07 Problem books
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