Recent Submissions

  • On global location-domination in graphs 

    Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel (2015-05-29)
    Article
    Open Access
    A dominating set S of a graph G is called locating-dominating, LD-set for short, if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S. Locating-dominating sets of minimum cardinality ...
  • Empty non-convex and convex four-gons in random point sets 

    Fabila Monroy, Ruy; Huemer, Clemens; Mitsche, Dieter (2015-03-01)
    Article
    Open Access
    Let S be a set of n points distributed uniformly and independently in a convex, bounded set in the plane. A four-gon is called empty if it contains no points of S in its interior. We show that the expected number of empty ...
  • Note on the number of obtuse angles in point sets 

    Fabila-Monroy, Ruy; Huemer, Clemens; Tramuns, Eulàlia (2014-09)
    Article
    Open Access
    In $1979$ Conway, Croft, Erd\H{o}s and Guy proved that every set $S$ of $n$ points in general position in the plane determines at least $\frac{n^3}{18}-O(n^2)$ obtuse angles and also presented a special set of $n$ points ...
  • Compatible spanning trees 

    Garcia Olaverri, Alfredo Martin; Huemer, Clemens; Hurtado Díaz, Fernando Alfredo; Tejel Altarriba, Francisco Javier (2014-07-01)
    Article
    Open Access
    Two plane geometric graphs are said to be compatible when their union is a plane geometric graph. Let S be a set of n points in the Euclidean plane in general position and let T be any given plane geometric spanning tree ...
  • Lower bounds for the number of small convex k-holes 

    Aichholzer, Oswin; Fabila Monroy, Ruy; Hackl, Thomas; Huemer, Clemens; Pilz, Alexander; Vogtenhuber, Birgit (2014-07-01)
    Article
    Open Access
    Let S be a set of n points in the plane in general position, that is, no three points of S are on a line. We consider an Erdos-type question on the least number h(k)(n) of convex k-holes in S, and give improved lower bounds ...
  • 4-Holes in point sets 

    Aichholzer, Oswin; Fabila Monroy, Ruy; Gonzalez Aguilar, Hernan; Hackl, Thomas; Heredia, Marco A.; Huemer, Clemens; Urrutia Galicia, Jorge; Vogtenhuber, Birgit (2014-08-01)
    Article
    Open Access
    We consider a variant of a question of Erdos on the number of empty k-gons (k-holes) in a set of n points in the plane, where we allow the k-gons to be non-convex. We show bounds and structural results on maximizing and ...
  • Empty monochromatic simplices 

    Aichholzer, Oswin; Fabila Monroy, Ruy; Hackl, Thomas; Huemer, Clemens; Urrutia Galicia, Jorge (2014-03-01)
    Article
    Open Access
    Let S be a k-colored (finite) set of n points in , da parts per thousand yen3, in general position, that is, no (d+1) points of S lie in a common (d-1)-dimensional hyperplane. We count the number of empty monochromatic ...
  • The number of empty four-gons in random point sets 

    Fabila-Monroy, Ruy; Huemer, Clemens; Mitsche, Dieter (2014)
    Article
    Open Access
    Let S be a set of n points distributed uniformly and independently in the unit square. Then the expected number of empty four-gons with vertices from S is T(n^2 log¿ n). A four-gon is empty if it contains no points of S ...
  • Witness rectangle graphs 

    Aronov, Boris; Dulieu, Muriel; Hurtado Díaz, Fernando Alfredo (2014-07)
    Article
    Restricted access - publisher's policy
    In a witness rectangle graph (WRG) on vertex point set P with respect to witness point set W in the plane, two points x, y in P are adjacent whenever the open isothetic rectangle with x and y as opposite corners contains ...
  • The degree/diameter problem in maximal planar bipartite graphs 

    Dalfó Simó, Cristina; Huemer, Clemens; Salas Piñon, Julián (2014)
    Article
    Open Access
    The (¿;D) (degree/diameter) problem consists of nding the largest possible number of vertices n among all the graphs with maximum degree ¿ and diameter D. We consider the (¿;D) problem for maximal planar bipartite graphs, ...

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