Ruy Fabila‐Monroy

activity

20122023

most citedOn

k

-Gons and

k

-Holes in Point Sets

3 citations · 4 across the 7 of their papers we have counts for

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4 papers · 1 filter

math.CO2023

A Note on the 2-Colored Rectilinear Crossing Number of Random Point Sets in the Unit Square

Sergio Cabello, Éva Czabarka, Ruy Fabila-Monroy +5

Let $S$ be a set of four points chosen independently, uniformly at random from a square. Join every pair of points of $S$ with a straight line segment. Color these edges red if the…

math.CO2014

$(n, m)$ -Fold Covers of Spheres

Imre Bárány, Ruy Fabila-Monroy, Birgit Vogtenhuber

A well known consequence of the Borsuk-Ulam theorem is that if the $d$ -dimensional sphere $S^{d}$ is covered with less than $d + 2$ open sets, then there is a set containing a pair of…

math.CO2014

Computational search of small point sets with small rectilinear crossing number

Ruy Fabila-Monroy, Jorge López

Let $\crs(K_n)$ be the minimum number of crossings over all rectilinear drawings of the complete graph on $n$ vertices on the plane. In this paper we prove that $\crs(K_n) < 0.3804…

math.CO2012

On the Connectedness and Diameter of a Geometric Johnson Graph

Crevel Bautista-Santiago, Javier Cano, Ruy Fabila-Monroy +5

Let $P$ be a set of $n$ points in general position in the plane. A subset $I$ of $P$ is called an \emph{island} if there exists a convex set $C$ such that $I = P \cap C$ . In this p…

A Note on the 2-Colored Rectilinear Crossing Number of Random Point Sets in the Unit Square

(n,m)-Fold Covers of Spheres

Computational search of small point sets with small rectilinear crossing number

On the Connectedness and Diameter of a Geometric Johnson Graph

$(n, m)$ -Fold Covers of Spheres