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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Elimination properties for minimal dominating sets of graphs
(20200101)
Article
Open AccessA dominating set of a graph is a vertex subset such that every vertexnot in the subset is adjacent to at least one in the subset. In this paper westudy whenever there exists a new dominating set contained (respectively, ... 
Total domination in plane triangulations
(20210101)
Article
Open AccessA total dominating set of a graph is a subset of such that every vertex in is adjacent to at least one vertex in . The total domination number of , denoted by , is the minimum cardinality of a total dominating set of . A ... 
Caterpillars are antimagic
(20210121)
Article
Restricted access  publisher's policyAn antimagic labeling of a 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 u is the sum of the labels assigned to the ... 
Reappraising the distribution of the number of edge crossings of graphs on a sphere
(Institute of Physics (IOP), 20200801)
Article
Restricted access  publisher's policyMany real transportation and mobility networks have their vertices placed on the surface of the Earth. In such embeddings, the edges laid on that surface may cross. In his pioneering research, Moon analyzed the distribution ... 
Neighborlocating colorings in graphs
(20200202)
Article
Open AccessA kcoloring of a graph G is a kpartition of into independent sets, called colors. A kcoloring is called neighborlocating if for every pair of vertices belonging to the same color , the set of colors of the neighborhood ... 
Total domination in plane triangulations
(20201109)
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