combinatorial geometry

The Double Cap Conjecture ★★

Author(s): Kalai



Point sets with no empty pentagon

Author(s): Wood

Problem   Classify the point sets with no empty pentagon.

Keywords: combinatorial geometry; visibility graph

Erdös-Szekeres conjecture ★★★

Author(s): Erdos; Szekeres

Conjecture   Every set of $ 2^{n-2} + 1 $ points in the plane in general position contains a subset of $ n $ points which form a convex $ n $-gon.

Keywords: combinatorial geometry; Convex Polygons; ramsey theory

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