Browsing by Author "Fabila Monroy, Ruy"
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4Holes in point sets
Aichholzer, Oswin; Fabila Monroy, Ruy; Gonzalez Aguilar, Hernan; Hackl, Thomas; Heredia, Marco A.; Huemer, Clemens; Urrutia Galicia, Jorge; Vogtenhuber, Birgit (20140801)
Article
Open AccessWe consider a variant of a question of Erdos on the number of empty kgons (kholes) in a set of n points in the plane, where we allow the kgons to be nonconvex. We show bounds and structural results on maximizing and ... 
Carathodory's theorem in depth
Fabila Monroy, Ruy; Huemer, Clemens (20170701)
Article
Open AccessLet 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 (201805)
Article
Open AccessWe 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 ... 
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)
Conference report
Open AccessWe study the cyclic sequences induced at in nity by pairwisedisjoint 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 ... 
EdgeRemoval and NonCrossing 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
Open AccessA 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 straightline 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 (20140301)
Article
Open AccessLet S be a kcolored (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 (d1)dimensional hyperplane. We count the number of empty monochromatic ... 
Empty nonconvex and convex fourgons in random point sets
Fabila Monroy, Ruy; Huemer, Clemens; Mitsche, Dieter (20150301)
Article
Open AccessLet S be a set of n points distributed uniformly and independently in a convex, bounded set in the plane. A fourgon 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 kholes
Aichholzer, Oswin; Fabila Monroy, Ruy; Hackl, Thomas; Huemer, Clemens; Pilz, Alexander; Vogtenhuber, Birgit (20140701)
Article
Open AccessLet 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 Erdostype question on the least number h(k)(n) of convex kholes 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)
Conference report
Restricted access  publisher's policyGiven an ordered set of points and an ordered set of geometric objects in the plane, we are interested in finding a noncrossing matching between pointobject 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)
Conference report
Open AccessWe 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 kgons and kholes 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 (20150801)
Article
Open AccessWe consider a variation of the classical ErdosSzekeres problems on the existence and number of convex kgons and kholes (empty kgons) in a set of n points in the plane. Allowing the kgons to be nonconvex, 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, 20210915)
Article
Open AccessWe study the Laplacian spectrum of token graphs, also called symmetric powers of graphs. The ktoken graph of a graph G is the graph whose vertices are the ksubsets 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)
Conference lecture
Restricted access  publisher's policyHow to draw the vertices of a complete multipartite graph G on different points of a bounded ddimensional 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, 20230718)
Article
Open AccessFor sets of n points, n even, in general position in the plane, we consider straightline 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; FernándezMerchant, Silvia; Flores Peñaloza, David; Hurtado Díaz, Fernando Alfredo; Meijer, Henk; Sacristán Adinolfi, Vera; Saumell Mendiola, Maria (2010)
Conference report
Open AccessGiven 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)
Conference report
Open AccessWe study the Laplacian spectrum of token graphs, also called symmetric powers of graphs. The ktoken graph Fk(G) of a graph G is the graph whose vertices are the ksubsets 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)
Conference report
Open AccessLet 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 ...