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Ponencia
Computing Optimal Shortcuts for Networks
(Dagsthul Publishing, 2018)
We study augmenting a plane Euclidean network with a segment, called shortcut, to minimize the largest distance between any two points along the edges of the resulting network. Questions of this type have received ...
Artículo
Euclidean position in Euclidean 2-orbifolds
(2004)
Intuitively, a set of sites on a surface is in Euclidean position if points are so close to each other that planar algorithms can be easily adapted in order to solve most of the classical problems in Computational Geometry. ...
Artículo
Cover contact graphs
(2012)
We study problems that arise in the context of covering certain geometric objects called seeds (e.g., points or disks) by a set of other geometric objects called cover (e.g., a set of disks or homothetic triangles). We ...
Artículo
Triangle-Free Planar Graphs as Segment Intersection Graphs
(2002)
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 and oblique) and in such a ...
Tesis Doctoral
Geometría computacional en superficies de órbitas
(2003)
En los casi treinta años de historia de la Geometría Computacional, sólo recientemente se han comenzado a estudiar problemas en superficies distintas del plano. Estudio que es necesario desde el momento en que surgen ...
Artículo
Dilation-free graphs in the l1 metric
(2007)
The dilation-free graph of a planar point set S is a graph that spans S in such a way that the distance between two points in the graph is no longer than their planar distance. Metrically speaking, those graphs are equivalent ...
Artículo
The difference between the metric dimension and the determining number of a graph
(2014)
We study the maximum value of the difference between the metric dimension and the determining number of a graph as a function of its order. We develop a technique that uses functions related to locating-dominating sets to ...
Artículo
Scutoids are a geometrical solution to three-dimensional packing of epithelia
(Nature Publishing Group, 2018)
As animals develop, tissue bending contributes to shape the organs into complex three-dimensional structures. However, the architecture and packing of curved epithelia remains largely unknown. Here we show by means of ...
Artículo
Transforming triangulations on non planar-surfaces
(2003)
We consider whether any two triangulations of a polygon or a point set on a non-planar surface with a given metric can be transformed into each other by a sequence of edge flips. The answer is negative in general with some ...