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Ponencia
On three parameters of invisibility graphs
(2013)
The invisibility graph I(X) of a set X ⊆ Rd is a (possibly infinite) graph whose vertices are the points of X and two vertices are connected by an edge if and only if the straight-line segment connecting the two corresponding ...
Ponencia
Empty convex polytopes in random point sets
(2013)
Given a set P of points in Rd, a convex hole (alternatively, empty convex polytope) of P is a convex polytope with vertices in P, containing no points of P in its interior. Let R be a bounded convex region in Rd. We show ...
Ponencia
Some results on open edge guarding of polygons
(2013)
This paper focuses on a variation of the Art Gallery problem that considers open edge guards. The “open” prefix means the endpoints of an edge where a guard is are not taken into account for visibility purposes. This paper ...
Ponencia
Improved enumeration of simple topological graphs
(2013)
A simple topological graph T = (V (T ), E(T )) is a drawing of a graph in the plane where every two edges have at most one common point (an endpoint or a crossing) and no three edges pass through a single crossing. Topological ...
Ponencia
Stackable tessellations
(2013)
We introduce a class of solids that can be constructed gluing stackable pieces, which has been proven to have advantages in architectural construction. We derive a necessary condition for a solid to belong to this class. ...