Seminar "Geometry and Combinatorics"

Tverberg-type theorems for balls

by Mr Olimjoni Pirahmad

Europe/Moscow
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Description

For a finite set S of points in R^d and a graph with vertices on S consider the balls with diameters induced by the edges. We show that for any set S in the plane R^2 there exists a Hamiltonian cycle for which these disks share a point. Also, we prove that for any even set S in R^d there exists a perfect matching for which these balls share a point. The first result improves a recent result of  Soberón and Tang.

 

Based on joint work with Alexandr Polyanskii