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The group seeks to delve into the study of a wide range of combinatorial and structural problems on point sets, such as Erdos-Szekeres 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 Erdos-Szekeres 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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Recent Submissions

  • Neighbor-locating colorings in graphs 

    Alcón, Liliana; Gutierrez, Marisa; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel (2020-02-02)
    Article
    Restricted access - publisher's policy
    A k-coloring of a graph G is a k-partition of into independent sets, called colors. A k-coloring is called neighbor-locating if for every pair of vertices belonging to the same color , the set of colors of the neighborhood ...
  • Total domination in plane triangulations 

    Claverol Aguas, Mercè; Garcia Olaverri, Alfredo Martin; Hernández Peñalver, Gregorio; Hernando Martín, María del Carmen; Maureso Sánchez, Montserrat; Mora Giné, Mercè; Tejel Altarriba, Francisco Javier (2020-11-09)
    External research report
    Open Access