
combinatorial geometry
The Double Cap Conjecture ★★
Author(s): Kalai
Conjecture The largest measure of a Lebesgue measurable subset of the unit sphere of
containing no pair of orthogonal vectors is attained by two open caps of geodesic radius
around the north and south poles.


Keywords: combinatorial geometry; independent set; orthogonality; projective plane; sphere
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 ★★★
Conjecture Every set of
points in the plane in general position contains a subset of
points which form a convex
-gon.



Keywords: combinatorial geometry; Convex Polygons; ramsey theory
