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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

  • Metric dimension of maximal outerplanar graphs 

    Claverol Aguas, Mercè; Hernando Martín, María del Carmen; Maureso Sánchez, Montserrat; Mora Giné, Mercè (2021-02-02)
    Article
    Restricted access - publisher's policy
    In 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 ...
  • Elimination properties for minimal dominating sets of graphs 

    Martí Farré, Jaume; Mora Giné, Mercè; Puertas González, María Luz; Ruiz Muñoz, José Luis (2020-01-01)
    Article
    Open Access
    A 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 

    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 (2021-01-01)
    Article
    Open Access
    A 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 

    Lozano Bojados, Antoni; Mora Giné, Mercè; Seara Ojea, Carlos; Tey Carrera, Joaquín (2021-01-21)
    Article
    Restricted access - publisher's policy
    An 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 

    Alemany Puig, Lluís; Mora Giné, Mercè; Ferrer Cancho, Ramon (Institute of Physics (IOP), 2020-08-01)
    Article
    Open Access
    Many 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 ...
  • 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
    Open Access
    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