1 citations · 1 across the 1 of their papers we have counts for
6 papers
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…
On the Number of Order Types in Integer Grids of Small Size
Luis E. Caraballo, José-Miguel Díaz-Báñez, Ruy Fabila-Monroy +3
Let and be two sets of labeled points in general position in the plane. We say that these two point sets have the same order type if for…
Drawing the Almost Convex Set in an Integer Grid of Minimum Size
Frank Duque, Ruy Fabila-Monroy, Carlos Hidalgo-Toscano +1
In 2001, Károlyi, Pach and Tóth introduced a family of point sets to solve an Erdős-Szekeres type problem; which have been used to solve several other Edős-Szekeres type problems.…