DCG  Discrete and Combinatorial Geometry

The group seeks to delve into the study of a wide range of combinatorial and structural problems on point sets, such as ErdosSzekeres type problems, problems of classical Euclidean geometry, problems in the spirit of Carathéodory’s theorem, problems on crossing numbers, or enumerative problems for geometric graphs of point sets. We also aim to obtain new insights into structural and geometric aspects of graphs/networks. We study combinatorial properties of graphs whose transposition to geometric graphs is of great interest: domination, location, covering, colorings,... This relationship between properties of combinatorial graphs and those of geometric graphs and point sets is also evident in the crucial fact that on the one hand, the study of combinatorial properties of graphs is eased by the study of their embeddings in the plane and, conversely, the study of sets of points –in the plane and in higher dimension– is eased by studying the graphs they determine.
The group seeks to delve into the study of a wide range of combinatorial and structural problems on point sets, such as ErdosSzekeres type problems, problems of classical Euclidean geometry, problems in the spirit of Carathéodory’s theorem, problems on crossing numbers, or enumerative problems for geometric graphs of point sets. We also aim to obtain new insights into structural and geometric aspects of graphs/networks. We study combinatorial properties of graphs whose transposition to geometric graphs is of great interest: domination, location, covering, colorings,... This relationship between properties of combinatorial graphs and those of geometric graphs and point sets is also evident in the crucial fact that on the one hand, the study of combinatorial properties of graphs is eased by the study of their embeddings in the plane and, conversely, the study of sets of points –in the plane and in higher dimension– is eased by studying the graphs they determine.
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Articles de revista [29]
Recent Submissions

Matching random colored points with rectangles
(Springer, 2020)
Conference report
Open AccessLet S[0,1]2 be a set of n points, randomly and uniformly selected. Let RB be a random partition, or coloring, of S in which each point of S is included in R uniformly at random with probability 1/2. We study the random ... 
The equidistant dimension of graphs
(20220506)
Article
Open AccessA subset S of vertices of a connected graph G is a distanceequalizer set if for every two distinct vertices x,y¿V(G)\S there is a vertex w¿S such that the distances from x and y to w are the same. The equidistant dimension ... 
Algorithmic geometry with infinite time computation
(2021)
Conference report
Restricted access  publisher's policy 
On maximumsum matchings of points
(2021)
Conference report
Restricted access  publisher's policyHuemer et al. (Discrete Math., 2019) proved that for any two point sets R and B with R = B, the perfect matching that matches points of R with points of B, and maximizes the total squared Euclidean distance of the ... 
Some results on the laplacian spectra of Token graphs
(Springer, 2021)
Conference report
Open AccessWe study the Laplacian spectrum of token graphs, also called symmetric powers of graphs. The ktoken graph Fk(G) of a graph G is the graph whose vertices are the ksubsets of vertices from G, two of which being adjacent ... 
The edge labeling of higher order Voronoi diagrams
(2021)
Conference report
Open AccessWe present an edge labeling of orderk Voronoi diagrams, Vk(S), of point sets S in the plane, and study properties of the regions defined by them. Among them, we show that Vk(S) has a small orientable cycle and path double ... 
On the Laplacian spectra of token graphs
(Elsevier, 20210915)
Article
Open AccessWe study the Laplacian spectrum of token graphs, also called symmetric powers of graphs. The ktoken graph of a graph G is the graph whose vertices are the ksubsets of vertices from G, two of which being adjacent whenever ... 
New cyclic Kautz digraphs with optimal diameter
(2021)
Article
Open AccessWe obtain a new family of digraphs with minimal diameter, that is, given the number of vertices and outdegree, there is no other digraph with a smaller diameter. This new family of digraphs are called `modified cyclic ... 
New production matrices for geometric graphs
(Elsevier, 20220115)
Article
Restricted access  publisher's policyWe use production matrices to count several classes of geometric graphs. We present novel production matrices for noncrossing partitions, connected geometric graphs, and kangulations, which provide another, simple and ... 
On circles enclosing many points
(20211001)
Article
Restricted access  publisher's policyWe prove that every set of n red and n blue points in the plane contains a red and a blue point such that every circle through them encloses at least points of the set. This is a twocolored version of a problem posed by ... 
Trees whose evendegree vertices induce a path are antimagic
(202208)
Article
Open AccessAn antimagic labeling of a connected graph G is a bijection from the set of edges E(G) to {1, 2, . . . , E(G)} such that all vertex sums are pairwise distinct, where the vertex sum at vertex v is the sum of the labels ... 
Metric dimension of maximal outerplanar graphs
(20210202)
Article
Open AccessIn this paper, we study the metric dimension problem in maximal outerplanar graphs. Concretely, if ß(G) denotes the metric dimension of a maximal outerplanar graph G of order n, we prove that 2=ß(G)=¿2n5¿ and that the ...