
ANDRÁS BEZDEK, The Mathematical Institute of the Hungarian Academy of Science, Budapest, Hungary, and Department of Mathematics, Auburn University, Auburn, Alabama 368495310, USA 
A Sylwester type theorem on circles 
In spite of the specific title, generalizations of two combinatorial geometric problems will be disscussed. The classical result of Sylvester shows that n points in the plane, not all on a common line, there exists an ordinary line (a line through exactly two points). The similar question about unit circles will be disscussed. A problem of V. Boltyanski (proved by A. V. Bogomolnaya, A. V. Nazarov and S. Rukshin) claims that if n points in a convex nsided polygon are given, then using the sides and the given points n sidepoint pairs can be formed such that the triangles determined by the pairs cover the convex polygon. We strengthen this result by proving that the assumption according to which the given points are inside of the polygon is redundant. We also give a bound for the number of disjoint such triangles.