We study the concept of the continuous mean distance of a weighted graph. For connected unweighted graphs, the mean distance ...

Apico-basal cell intercalations (scutoids) optimize packing and energy expenditure in curved epithelia. Further consequences ...

We have introduced here the concept of Hamiltonian triangular refinement. For any Hamiltonian triangulation it is shown ...

As animals develop, tissue bending contributes to shape the organs into complex three-dimensional structures. However, the ...

We study augmenting a plane Euclidean network with a segment, called shortcut, to minimize the largest distance between ...

We study the problem of augmenting the locus N of a plane Euclidean network N by in- serting iteratively a finite set ...

We present a new approach to adapt the differential evolution (DE) algorithm so that it can be applied in combinatorial ...

We study the relation between algebraic structures and Graph Theory. We have de ned ve di erent weighted digraphs associated ...

We study the problem of augmenting the locus N of a plane Euclidean network N by inserting iteratively a finite set of ...

Con la idea de modelar el comportamiento de diversas redes sociales a lo largo del tiempo, mostramos algunos resultados ...

Given a bicolored point set S, it is not always possible to construct a monochromatic geometric planar k-factor of S. We ...

A new edge-based partition for triangle meshes is presented, the Seven Triangle Quasi-Delaunay partition (7T-QD). The ...

We study the maximum value of the difference between the metric dimension and the determining number of a graph as a ...

We describe an algorithm to compute the Tutte polynomial of large fragments of Archimedean tilings by squares, triangles, ...

This paper deals with the maximum value of the difference between the determining number and the metric dimension of a ...

A set of vertices SS in a graph GG is a resolving set for GG if, for any two vertices u,vu,v, there exists x∈Sx∈S such ...

This paper deals with three resolving parameters: the metric dimension, the upper dimension and the resolving number. We ...

Bar visibility graphs were introduced in the seventies as a model for some VLSI layout problems. They have been also studied ...

Let P and F be sets of n ≥ 2 and m ≥ 2 points in the plane, respectively, so that P∪F is in general position. We study the ...

In 1958, Hill conjectured that the minimum number of crossings in a drawing of Kn is exactly Z(n) = 1/4 n-1/2/2 n−2/2 ...

Let f(n) be a function and L be a graph. Denote by RT(n, L, f(n)) the maximum number of edges of an L-free graph on n ...

Given a set S of n points in the plane, in this paper we give a necessary and sometimes sufficient condition to build a 4-connected non-crossing geometric graph on S.

In this paper we consider the flip operation for combinatorial pointed pseudo-triangulations where faces have size 3 or ...

We study a graph parameter related to resolving sets and metric dimension, namely the resolving number, introduced by ...

A set of vertices S is a determining set of a graph G if every automorphism of G is uniquely determined by its action on ...

This paper focuses on a variation of the Art Gallery problem that considers open edge guards. The “open” prefix means the ...

Abstract Voronoi diagrams are a unifying framework that covers many types of concrete Voronoi diagrams. This talk reports on the state of the art, including recent progress.

Let G be a graph embedded in an orientable surface Σ, possibly with edge weights, and denote by len(γ) the length (the ...

A triangulation of a surface is irreducible if there is no edge whose contraction produces another triangulation of the ...

A d-dimensional simplex S is called a k-reptile (or a k-reptile simplex) if it can be tiled without overlaps by k simplices ...

An intriguing conjecture of Nandakumar and Ramana Rao is that for every convex body K ⊆ R2, and for any positive integer ...

Sensory evaluation of foods is as important as chemical, physical or microbiological examinations, being specially relevant ...

A web-based system that determines point/curve and curve/curve bisectors in a dynamic geometry system in a completely ...

In 1926, Jarník introduced the problem of drawing a convex n-gon with vertices having integer coordinates. He constructed ...

The Minimum Weight Pseudo-Triangulation (MWPT) problem is suspected to be NP-hard. We show here how Simulated Annealing ...

We present a practical Java tool for simulating synchronized distributed algorithms on sets of 2-and 3-dimensional ...

Given a set P of points in Rd, a convex hole (alternatively, empty convex polytope) of P is a convex polytope with vertices ...

In 1979 Conway, Croft, Erd\H{o}s and Guy proved that every set SS of nn points in general position in the plane determines ...

Let S be a set of n points in Rd in general position. A set H of k-flats is called an mk-stabber of S if the relative ...

We introduce a class of solids that can be constructed gluing stackable pieces, which has been proven to have advantages ...

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 ...

An orthogonal polygon of P is called “thin” if the dual graph of the partition obtained by extending all edges of P towards ...

In this paper we study the problem of finding flock patterns in a set of trajectories of moving entities. A flock refers ...

In this paper we propose and solve common influence region queries. We present GPU parallel algorithms, designed under ...

In this paper we propose a new GPU method able to compute the 2D constrained Delaunay triangulation of a planar straight ...

We focus on the development of approximated algorithms to find high quality triangulations of minimum dilation because the ...

Based on some recent modelling considerations in location theory we call for study of three CG constructs of Voronoi type that seem not to have been studied much before.

Given an arrangement A of n sensors and two points s and t in the plane, the barrier resilience of A with respect to s and ...

Although the exact counting and enumeration of polyominoes remain challenging open problems, several positive results were ...

In this paper we de ne a distance guarding concept on plane graphs and associate this concept with distance domination and ...

The invisibility graph I(X) of a set X ⊆ Rd is a (possibly infinite) graph whose vertices are the points of X and two ...

A graph is crossing-critical if its crossing number decreases when we remove any of its edges. Recently it was proved that ...

Bar visibility graphs were introduced in the seventies as a model for some VLSI layout problems. They have been also studied ...

It is well known that, given n red points and n blue points on a circle, it is not always possible to find a plane geometric ...

In this paper, we introduce a natural variation of the problem of computing all bichromatic intersections between two sets ...

Let R and B be sets of red and blue points in the plane in general position. We study the problem of computing a k-level ...

We study problems that arise in the context of covering certain geometric objects called seeds (e.g., points or disks) by ...

Dominating concepts constitute a cornerstone in Graph Theory. Part of the efforts in the field have been focused in finding ...

The problem of computing a representation of the stabbing lines of a set S of segments in the plane was solved by Edelsbrunner ...

The Erdös–Sós conjecture says that a graph G on n vertices and number of edges e(G) > n(k − 1)/2 contains all trees of ...

This paper proves that the Di erential Evolution (DE) algorithm is valid to solve the Shortest Path (SP) problem in random, median sized networks. From the trials, we have obtained an 9% accuracy, in the worst case scenario.

A graph G is said to be grid locatable if it admits a representation such that vertices are mapped to grid points and edges ...

The ϵ-Depth ANT Explorer (ϵ- DANTE ) algorithm applied to a multiple objective optimization problem is presented in this ...

We consider whether any two triangulations of a polygon or a point set on a nonplanar surface with a given metric can be ...

We study the existence of monochromatic planar geometric k-factors on sets of red and blue points. When it is not possible ...

The triangle longest-edge bisection constitutes an efficient scheme for refining a mesh by reducing the obtuse triangles, ...

We use the Steiner distance to define a convexity in the vertex set of a graph, which has a nice behavior in the well-known ...

A new triangle partition, the seven-triangle longest-edge partition, based on the trisection of the edges is presented and ...

A Möbius triangulation is a triangulation on the Möbius band. A geometric realization of a map M on a surface $\Sigma$ is ...

The isin-DANTE method is an hybrid meta-heuristic. In combines the evolutionary ant colony optimization (ACO) algorithms ...

El estudio de soluciones meta-heurísticas basadas en el paradigma del Ant Colony Optimization (ACO) para el Multiple ...

En este trabajo estudiamos el problema de determinar si dos conjuntos disjuntos de n puntos en el plano son separables ...

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 ...

We study problems that arise in the context of covering certain geometric objects (so-called seeds, e.g., points or disks) ...

The new approach we propose in this paper is a plane partition with similar features to those of the Voronoi Diagram, but ...

The usual distance between pairs of vertices in a graph naturally gives rise to the notion of an interval between a pair ...

We give a complete classification of hexagonal tilings and locally C6 graphs, by showing that each of them has a natural ...

We develop the necessary machinery in order to prove that hexagonal tilings are uniquely determined by their Tutte polynomial, showing as an example how to apply this technique to the toroidal hexagonal tiling.

The NP multiple criteria minimum spanning tree as several applications into the network design problems. In this paper, ...

Any metric quadrangulation (made by segments of straight line) of a point set in the plane determines a 2-coloration of ...

En eta memoria estudiamos diversos aspectos del polinomio de Tutte de una teselación regular. Comenzamos introduciendo ...

Intuitively, a set of sites on a surface is in Euclidean position if points are so close to each other that planar algorithms ...

The exact values of the function $ex(n;TK_{p})$ are known for ${\lceil \frac{2n+5}{3}\rceil}\leq p < n$ (see [Cera, Diánez, ...

A graph is said to be locally grid if the structure around each of its vertices is a 3 × 3 grid. As a follow up of the ...

We define a locally grid graph as a graph in which the structure around each vertex is a 3×3 grid ⊞, the canonical examples ...

In this work we study more questions about spanners in the l1-metric. Concretely, we will see that adding some Steiner ...

Motion planning and visibility problems are some of the most important topics studied in Computer Graphics, Computational ...

The Ant Colony Optimisation Algorithm (ACO) supports the development of a system for a multi-objective network ...

In this paper we present an Ant Colony Optimisation based algorithm to determine the Pareto set for the Multiple Objective Travelling Salesman Problem. Our results are then compared with the ones obtained with a genetic algorithm.

We consider whether any two triangulations of a polygon or a point set on a non-planar surface with a given metric can be ...

En los casi treinta años de historia de la Geometría Computacional, sólo recientemente se han comenzado a estudiar problemas ...

We prove that every triangle-free planar graph is the intersection graph of a set of segments in the plane. Moreover, the ...

The following problem of rectilinear routing is studied: given pairs of points on a surface and a set of permissible ...

The results we introduce in this work lead to get an algorithm which produces aperiodic sets of tiles using Voronoi diagrams. ...

We show that any two outer-triangulations on the same closed surface can be transformed into each other by a sequence of diagonal flips, up to isotopy, if they have a sufficiently large and equal number of vertices.

El etiquetado es una de las grandes áreas de investigación dentro de la Geometría Computacional. Así lo avalan, tanto la ...

In this note we show that 1-skeletons and 2-skeletons of n-pseudomanifolds with full boundary are (n+ 1)-connected graphs and n-connected 2-complexes, respectively. This generalizes previous results due to Barnette and Woon.

El área de investigación sobre dibujos de grafos constituye una importante conexión entre diversos campos de la Matemática, ...

Chartrand et al. (J. Combin. Theory Ser. B 10 (1971) 12–41) proved that the line graph of a graph G is outerplanar if and ...

Graphical features on map, charts, diagrams and graph drawings usually must be annotated with text labels in order to ...

In this note we show a new upperbound for the function ex(n;TKp), i.e., the maximum number of edges of a graph of order n ...

El matemático alemán Euler (1707-1782) resolvió en 1736 el famoso problema de los puentes de Königsberg. Dicha ciudad ...

Given a set P of points in the plane, the geometric tree graph of P is defined as the graph T(P) whose vertices are ...

We prove that every triangle-free planar graph is the graph of intersection of a set of segments in the plane. Moreover, ...

This paper contains a study of the connectivity of infinite graphs and 2-complexes. Various connectivity types are defined ...

El área de investigación sobre dibujos de grafos, la Teoría Topológica de Grafos, constituye una importante conexión entre ...

De forma general, la Geometría Computaciones trata del estudio de algoritmos que resuelven problemas geométricos con el ...

"Desde el origen de la Teoría de Grafos Extremales, uno de los problemas más generales que pueden plantearse en este campo, ...

This paper is devoted to the study of graph embeddings in the grid of non-planar surfaces. We provide an adequate model ...

Se generaliza el concepto de anchura de un conjunto en el plano a la superficie de la esfera, dando condiciones necesarias ...

In this work, we get a combinatorial characterization for maximal generalized outerplanar graphs (mgo graphs). This result yields a recursive algorithm testing whether a graph is a mgo graph or not.

El área de investigación sobre dibujos de grafos (graph drawing) se ha convertido en un campo extensamente estudiado, ...

In this note we extend the notion of the center of a graph to infinite graphs. Thus, a vertex is in the center of the ...

We give a visibility representation of graphs which extends some very well-known representations considered extensively ...

"Si bien el problema de la Transversalidad ha sido ampliamente estudiado en la Teoría de Grafos, los 2-complejos de Euler ...

Tres son los problemas fundamentales que presenta el estudio de los grafos de visibilidad: el de la construcción, el de ...

Moore spaces are de ned in proper homotopy theory. Some results on the existence and uniqueness of those spaces are proven. An example of two non properly equivalent Moore spaces is given.

El objetivo de esta Tesis es definir una familia de grafos infinitos en la cual es posible construir una algorítmica finita. ...

In this Note, we study infinite graphs with locally finite outerplane embeddings, given a characterization by forbidden subgraphs

Los primeros problemas que plantearon y resolvieron en Teoría de Grafos, son problemas referentes a la Transversalidad de ...

The main goal of this paper is to show the functional architecture of a framework for digital topology. This architecture ...

In this Note, we study some properties of Sedlacek's C-graphs (see [3], [4] and [5]). In particular, we give new methods ...

We introduce and study proper homotopy invariants of the Lusternik-Schnirelmann type, p-cat (-), p-Cat(-), and cat e(-) ...

This work presents a classification of the proper homotopy types of locally finite 1-dimensional CW-complexes.

En el Capítulo 1, vamos a desarrollar el concepto de aplicaciones up (uniformemente continuas y propias) entre espacios ...