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math.MG2013
The Colored Hadwiger Transversal Theorem in
Andreas F. Holmsen, Edgardo Roldán-Pensado
Hadwiger's transversal theorem gives necessary and sufficient conditions for a family of convex sets in the plane to have a line transversal. A higher dimensional version was obtai…
math.MG2013
Erdős - Szekeres Theorem for Lines
Imre Bárány, Edgardo Roldán-Pensado, Géza Tóth
According to the Erdős-Szekeres theorem, for every , a sufficiently large set of points in general position in the plane contains in convex position. In this note we investi…
math.MG2013
Paths on the Doubly Covered Region of a Covering of the Plane by Unit Discs
Edgardo Roldán-Pensado
Given a covering of the plane by closed unit discs and two points and in the region doubly covered by , what is the length of the shortest path con…