We prove that every triangle-free planar graph is the intersection graph of a set of segments in the plane. Moreover, the segments can be chosen in only three directions (horizontal, vertical andâ€¦ (More)

We show that many classical problems of Computational Geometry can be solved in the cylinder, but planar techniques cannot be adapted always successfully and new techniques must be considered.

We present an algorithm that computes the diameter of a set of n points in the cylinder in optimal time O(n log n); this algorithm uses as a fundamental tool the farthest point Voronoi diagram.

We study the relationship between some alternative definitions of the concept of the width of a convex set on the sphere. Those relations allow to characterize whether a convex set on the sphere canâ€¦ (More)

We give a visibility representation of graphs which extends some very well-known representations considered extensively in the literature. Concretely, the vertices are represented by a collection ofâ€¦ (More)

Dynamic graphs are locally nite, innnite graphs consisting of an innnite number of representations of a nite graph. The nature of these repetitions determines the dimension of a dynamic graph. Thisâ€¦ (More)

We prove that every triangle-free planar graph is the graph of intersection of a set of segments in the plane. Moreover, the segments can be chosen in only three directions (horizontal, vertical andâ€¦ (More)

We give a visibility representation of graphs which extends some very well-known representations considered extensively in the literature. Concretely, the vertices are represented by a collection ofâ€¦ (More)