R. Fabila-Monroy

activity

20122026

most citedPoint Sets with Small Integer Coordinates and with Small Convex Polygons

2 citations · 4 across the 10 of their papers we have counts for

collaborators

11 papers

math.CO2026

Automorphisms of Token Graphs That Send $4$ -Cycles Generated by Two Edges to Cycles Generated by a $4$ -Cycle and Two Tokens

Ruy Fabila-Monroy, Sergio Gerardo Gómez-Galicia, Ana Laura Trujillo-Negrete

Let $G$ be a connected graph. The $k$ -token graph of $G$ is the graph $F_{k} (G)$ whose vertex set consists of all subsets of $k$ vertices of $G$ , where two of them are adjacent whene…

math.CO2024

On the Automorphisms of Token Graphs Generated by $2$ -cuts with the Same Neighbours

Ruy Fabila-Monroy, Sergio Gerardo Gómez-Galicia, Daniel Gregorio-Longino +2

Let $G$ be a connected graph on $n$ vertices and $1 \leq k \leq n - 1$ an integer. The $k$ -token graph of $G$ is the graph $F_{k} (G)$ whose vertices are all the $k$ -subsets of vertices o…

math.CO2023

A Note on the Asymptotic Value of the Isoperimetric Number of $J (n, 2)$

Ruy Fabila-Monroy, Daniel Gregorio-Longino

Let $G$ be a graph on $n$ vertices and $S$ a subset of vertices of $G$ ; the boundary of $S$ is the set, $\partial S$ , of edges of $G$ connecting $S$ to its complement in $G$ . The…

math.CO2023

On the Automorphism Group of Token Graphs of Complete Bipartite Graphs

Ruy Fabila-Monroy, Ana Laura Trujillo-Negrete

Let $G$ be a graph of order $n$ and let $k \in {1, 2, \dots, n - 1}$ . The $k$ -token graph of $G$ is the graph, whose vertices are all the $k$ -subsets of vertices of $G$ , where two suc…

cs.CG2022

No Selection Lemma for Empty Triangles

Ruy Fabila-Monroy, Carlos Hidalgo-Toscano, Daniel Perz +1

Let $S$ be a set of $n$ points in general position in the plane. The Second Selection Lemma states that for any family of $Θ (n^{3})$ triangles spanned by $S$ , there exists a point of…

cs.RO2022

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…

cs.CG2020

A Note on Empty Balanced Tetrahedra in Two colored Point sets in $R^{3}$

José M. Díaz-Bañez, Ruy Fabila-Monroy, Jorge Urrutia

Let $S$ be a set of $n$ red and $n$ blue points in general position in $R^{3}$ . Let $τ$ be a tetrahedra with vertices on $S$ . We say that $τ$ is \emph{empty} if it does not…

math.CO2017★ 2 cited

The Chromatic Number of the Disjointness Graph of the Double Chain

Ruy Fabila-Monroy, Carlos Hidalgo-Toscano, Jesús Leaños +1

Let $P$ be a set of $n \geq 4$ points in general position in the plane. Consider all the closed straight line segments with both endpoints in $P$ . Suppose that these segments are co…

math.CO2016★ 2 cited

Point Sets with Small Integer Coordinates and with Small Convex Polygons

Frank Duque, Ruy Fabila-Monroy, Carlos Hidalgo-Toscano

In 1935, Erdős and Szekeres proved that every set of $n$ points in general position in the plane contains the vertices of a convex polygon of $\frac{1}{2} lo g_{2} (n)$ vertices. In 19…

cs.CG2015

Caratheodory's Theorem in Depth

Ruy Fabila-Monroy, Clemens Huemer

Let $X$ be a finite set of points in $R^{d}$ . The Tukey depth of a point $q$ with respect to $X$ is the minimum number $τ_{X} (q)$ of points of $X$ in a halfspace containing $q…

math.CO2012

Empty Monochromatic Simplices

Oswin Aichholzer, Ruy Fabila-Monroy, Thomas Hackl +2

Let $S$ be a $k$ -colored (finite) set of $n$ points in $R^{d}$ , $d \geq 3$ , in general position, that is, no { $(d + 1)$ } points of $S$ lie in a common $(d - 1)$ }-dimensional…

Automorphisms of Token Graphs That Send 4-Cycles Generated by Two Edges to Cycles Generated by a 4-Cycle and Two Tokens

On the Automorphisms of Token Graphs Generated by 2-cuts with the Same Neighbours

A Note on the Asymptotic Value of the Isoperimetric Number of J(n,2)