7 citations · 14 across the 9 of their papers we have counts for
13 papers
No Selection Lemma for Empty Triangles
Ruy Fabila-Monroy, Carlos Hidalgo-Toscano, Daniel Perz +1
Let be a set of points in general position in the plane. The Second Selection Lemma states that for any family of triangles spanned by , there exists a point of…
Stochastic strategies for patrolling a terrain with a synchronized multi-robot system
Luis E. Caraballo, José M. Díaz-Báñez, Ruy Fabila-Monroy +1
A group of cooperative aerial robots can be deployed to efficiently patrol a terrain, in which each robot flies around an assigned area and shares information with the neighbors pe…
Chirotopes of Random Points in Space are Realizable on a Small Integer Grid
Jean Cardinal, Ruy Fabila-Monroy, Carlos Hidalgo-Toscano
We prove that with high probability, a uniform sample of points in a convex domain in can be rounded to points on a grid of step size proportional to $1/n^{d+1+ε…
On the 2-colored crossing number
Oswin Aichholzer, Ruy Fabila-Monroy, Adrian Fuchs +4
Let be a straight-line drawing of a graph. The rectilinear 2-colored crossing number of is the minimum number of crossings between edges of the same color, taken over all p…
An Ongoing Project to Improve the Rectilinear and the Pseudolinear Crossing Constants
Oswin Aichholzer, Frank Duque, Ruy Fabila-Monroy +2
A drawing of a graph in the plane is {\it pseudolinear} if the edges of the drawing can be extended to doubly-infinite curves that form an arrangement of pseudolines, that is, any…
Counting the Number of Crossings in Geometric Graphs
Frank Duque, Ruy Fabila-Monroy, César Hernández-Vélez +1
A geometric graph is a graph whose vertices are points in general position in the plane and its edges are straight line segments joining these points. In this paper we give an $O(n…