Ara es mostren els items 1-17 de 17

    • 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
      Accés obert
      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 ...
    • Carathodory's theorem in depth 

      Fabila Monroy, Ruy; Huemer, Clemens (2017-07-01)
      Article
      Accés obert
      Let X be a finite set of points in RdRd . The Tukey depth of a point q with respect to X is the minimum number tX(q)tX(q) of points of X in a halfspace containing q. In this paper we prove a depth version of Carathéodory’s ...
    • Colored Ray configurations 

      Fabila Monroy, Ruy; Garcia Olaverri, Alfredo Martin; Hurtado Díaz, Fernando Alfredo; Jaume, Rafel; Pérez Lantero, Pablo; Saumell, Maria; Silveira, Rodrigo Ignacio; Tejel Altarriba, Francisco Javier; Urrutia Galicia, Jorge (2014)
      Text en actes de congrés
      Accés obert
      We study the cyclic sequences induced at in nity by pairwise-disjoint colored rays with apices on a given bal- anced bichromatic point set, where the color of a ray is inherited from the color of its apex. We derive a lower ...
    • Colored ray configurations 

      Fabila Monroy, Ruy; Garcia Olaverri, Alfredo Martin; Hurtado Díaz, Fernando Alfredo; Jaume, Rafel; Pérez Lantero, Pablo; Saumell, Maria; Silveira, Rodrigo Ignacio; Tejel Altarriba, Francisco Javier; Urrutia Galicia, Jorge (2018-05)
      Article
      Accés obert
      We study the cyclic color sequences induced at infinity by colored rays with apices being a given balanced finite bichromatic point set. We first study the case in which the rays are required to be pairwise disjoint. We ...
    • Edge-Removal and Non-Crossing Configurations in Geometric Graphs 

      Aichholzer, Oswin; Cabello, Sergio; Fabila Monroy, Ruy; Flores Peñaloza, David; Hackl, Thomas; Huemer, Clemens; Hurtado Díaz, Fernando Alfredo; Wood, David (2010)
      Article
      Accés obert
      A geometric graph is a graph G = (V;E) drawn in the plane, such that V is a point set in general position and E is a set of straight-line segments whose endpoints belong to V . We study the following extremal problem for ...
    • Empty monochromatic simplices 

      Aichholzer, Oswin; Fabila Monroy, Ruy; Hackl, Thomas; Huemer, Clemens; Urrutia Galicia, Jorge (2014-03-01)
      Article
      Accés obert
      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 ...
    • Empty non-convex and convex four-gons in random point sets 

      Fabila Monroy, Ruy; Huemer, Clemens; Mitsche, Dieter (2015-03-01)
      Article
      Accés obert
      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 ...
    • 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
      Accés obert
      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 ...
    • Matching points with things 

      Taslakian, Perouz; Seara Ojea, Carlos; Saumell Mendiola, Maria; Langerman, Stefan; Hurtado Díaz, Fernando Alfredo; Aloupis, Greg; Cardinal, Jean; Collette, Sébastien; Demaine, Erik D.; Demaine, Martin L.; Dulieu, Muriel; Fabila Monroy, Ruy; Hart, Vi (Springer Verlag, 2010)
      Text en actes de congrés
      Accés restringit per política de l'editorial
      Given an ordered set of points and an ordered set of geometric objects in the plane, we are interested in finding a non-crossing matching between point-object pairs. We show that when the objects we match the points to ...
    • Modem illumination of monotone polygons 

      Aichholzer, Oswin; Fabila Monroy, Ruy; Flores Peñaloza, David; Hackl, Thomas; Huemer, Clemens; Urrutia Galicia, Jorge; Vogtenhuber, Birgit (2009)
      Text en actes de congrés
      Accés obert
      We study a generalization of the classical problem of illumination of polygons. Instead of modeling a light source we model a wireless device whose radio signal can penetrate a given number k of walls. We call these ...
    • On k-gons and k-holes in point sets 

      Aichholzer, Oswin; Fabila Monroy, Ruy; Gonzalez Aguilar, Hernan; Hackl, Thomas; Heredia, Marco A.; Huemer, Clemens; Urrutia Galicia, Jorge; Valtr, Pavel; Vogtenhuber, Birgit (2015-08-01)
      Article
      Accés obert
      We consider a variation of the classical Erdos-Szekeres problems on the existence and number of convex k-gons and k-holes (empty k-gons) in a set of n points in the plane. Allowing the k-gons to be non-convex, we show ...
    • 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
      Accés obert
      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 ...
    • Optimal grid drawings of complete multipartite graphs and an integer variant of the algebraic connectivity 

      Fabila Monroy, Ruy; Hidalgo Toscano, Carlos; Huemer, Clemens; Lara, Dolores; Mitsche, Dieter (Springer, 2018)
      Comunicació de congrés
      Accés restringit per política de l'editorial
      How to draw the vertices of a complete multipartite graph G on different points of a bounded d-dimensional integer grid, such that the sum of squared distances between vertices of G is (i) minimized or (ii) maximized? For ...
    • Perfect matchings with crossings 

      Aichholzer, Oswin; Fabila Monroy, Ruy; Kindermann, Philipp; Parada Muñoz, Irene María de; Paul, Rosna; Perz, Daniel; Schnider, Patrick; Vogtenhuber, Birgit (Springer Nature, 2023-07-18)
      Article
      Accés obert
      For sets of n points, n even, in general position in the plane, we consider straight-line drawings of perfect matchings on them. It is well known that such sets admit at least Cn/2 different plane perfect matchings, where ...
    • Proximity graphs inside large weighted graphs 

      Ábrego, Bernardo M.; Fabila Monroy, Ruy; Fernández-Merchant, Silvia; Flores Peñaloza, David; Hurtado Díaz, Fernando Alfredo; Meijer, Henk; Sacristán Adinolfi, Vera; Saumell Mendiola, Maria (2010)
      Text en actes de congrés
      Accés obert
      Given a large weighted graph G = (V;E) and a subset U of V , we de¯ne several graphs with vertex set U in which two vertices are adjacent if they satisfy some prescribed proximity rule. These rules use the shortest path ...
    • 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)
      Text en actes de congrés
      Accés obert
      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 connectivity of the flip graph of Hamiltonian paths of the grid graph 

      Duque, Frank; Fabila Monroy, Ruy; Flores Peñazola, David; Hidalgo Toscano, Carlos; Huemer, Clemens (2017)
      Text en actes de congrés
      Accés obert
      Let Gn,m be the grid graph with n columns and m rows. Let Hn,m be the graph whose vertices are the Hamiltonian paths in Gn,m, where two vertices P1 and P2 are adjacent if we can obtain P2 from P1 by deleting an edge in P1 ...