Type: Article

Paths on the doubly covered region of a covering of the plane by unit discs

Roldán-Pensado, Edgardo;

Abstract:

Given a covering of the plane by closed unit discs F and two points A and B in the region doubly covered by F, what is the length of the shortest path connecting them that stays within the doubly covered region? This is a problem of G. Fejes-Tóth and he conjectured that if the distance between A and B is d, then the length of this path is at most 2–?d+O(1). In this paper we give a bound of 2.78d+O(1).