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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.

Recent Submissions

  • Matching random colored points with rectangles 

    Corujo, Josué; Flores Peñaloza, David; Huemer, Clemens; Seara Ojea, Carlos; Pérez Lantero, Pablo (Springer, 2020)
    Conference report
    Open Access
    Let 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 

    González Herrera, Antonio; Hernando Martín, María del Carmen; Mora Giné, Mercè (2022-05-06)
    Article
    Open Access
    A subset S of vertices of a connected graph G is a distance-equalizer 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 

    Huemer, Clemens; Muller, Moritz Martin; Seara Ojea, Carlos; Tobar Nicolau, Adrián (2021)
    Conference report
    Restricted access - publisher's policy
  • On maximum-sum matchings of points 

    Bereg, Sergey; Chacón Rivera, Oscar; Flores Peñaloza, David; Huemer, Clemens; Pérez Lantero, Pablo; Seara Ojea, Carlos (2021)
    Conference report
    Restricted access - publisher's policy
    Huemer 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 

    Dalfó Simó, Cristina; Duque, Frank; Fabila Monroy, Ruy; Fiol Mora, Miquel Àngel; Huemer, Clemens; Trujillo Negrete, Ana Laura; Zaragoza Martínez, Francisco (Springer, 2021)
    Conference report
    Restricted access - publisher's policy
    We study the Laplacian spectrum of token graphs, also called symmetric powers of graphs. The k-token graph Fk(G) of a graph G is the graph whose vertices are the k-subsets of vertices from G, two of which being adjacent ...
  • The edge labeling of higher order Voronoi diagrams 

    Claverol Aguas, Mercè; de las Heras Parrilla, Andrea; Huemer, Clemens; Martínez Moraian, Alejandra (2021)
    Conference report
    Open Access
    We present an edge labeling of order-k 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 

    Dalfó Simó, Cristina; Duque, Frank; Fabila Monroy, Ruy; Fiol Mora, Miquel Àngel; Huemer, Clemens; Trujillo Negrete, Ana Laura; Zaragoza Martínez, Francisco (Elsevier, 2021-09-15)
    Article
    Restricted access - publisher's policy
    We study the Laplacian spectrum of token graphs, also called symmetric powers of graphs. The k-token graph of a graph G is the graph whose vertices are the k-subsets of vertices from G, two of which being adjacent whenever ...
  • New cyclic Kautz digraphs with optimal diameter 

    Böhmová, Katerina; Dalfó Simó, Cristina; Huemer, Clemens (2021)
    Article
    Open Access
    We obtain a new family of digraphs with minimal diameter, that is, given the number of vertices and out-degree, there is no other digraph with a smaller diameter. This new family of digraphs are called `modified cyclic ...
  • New production matrices for geometric graphs 

    Esteban Pascual, Guillermo; Huemer, Clemens; Silveira, Rodrigo Ignacio (Elsevier, 2022-01-15)
    Article
    Restricted access - publisher's policy
    We use production matrices to count several classes of geometric graphs. We present novel production matrices for non-crossing partitions, connected geometric graphs, and k-angulations, which provide another, simple and ...
  • On circles enclosing many points 

    Claverol Aguas, Mercè; Huemer, Clemens; Martínez Moraian, Alejandra (2021-10-01)
    Article
    Restricted access - publisher's policy
    We 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 two-colored version of a problem posed by ...
  • Trees whose even-degree vertices induce a path are antimagic 

    Lozano Boixadors, Antoni; Mora Giné, Mercè; Seara Ojea, Carlos; Tey Carrera, Joaquín (2022-08)
    Article
    Open Access
    An 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 

    Claverol Aguas, Mercè; Hernando Martín, María del Carmen; Maureso Sánchez, Montserrat; Mora Giné, Mercè (2021-02-02)
    Article
    Open Access
    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 ...

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