In this survey talk, I collect a lot of results from discrete and computational geometry, explaining the special role that 'touchings' (tangencies) play in te subject. These questions contributed to the early development of the theory of Davenport-Schinzel sequences, algorithmic motion planning, geometric graph theory, and incidence geometry. We...
Creator:
Pach, Jà¡nos (École Polytechnique Fédérale de Lausanne (EPFL))
Created:
2014-11-11
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
A set system is a k-fold covering of space if every point is contained in at least k sets. A 1-fold covering is called simply a covering. In 1980, motivated by a question of Laszlo Fejes Toth, I raised the following question. Given a plane convex set C, does there exist an integer k=k(C) such that every k-fold covering of the plane splits into 2...
Creator:
Pach, Jà¡nos (École Polytechnique Fédérale de Lausanne (EPFL))
Created:
2014-09-10
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.