R. Fabila-Monroy

activity

20092026

most citedToken Graphs

65 citations · 165 across the 33 of their papers we have counts for

collaborators

41 papers

math.CO2026

Blow-ups of order types of positive density

Ruy Fabila-Monroy, Benedikt Hahn, Jesús Leaños

Order types are an equivalence relation between point configurations that capture their combinatorial and convexity properties. Let $P$ be a $κ$ -colored sequence of $n \geq d + 1$ poi…

math.CO2025

Domination number of Token Graphs

Ruy Fabila-Monroy, Sergio Gerardo Gómez-Galicia

The $k$ -token graph of $G$ is the graph, $F_{k} (G)$ , whose vertices are all the $k$ -subsets of $V (G)$ ; with two of them adjacent whenever their symmetric difference is a pair of adja…

cs.CG2025

The Euclidean $k$ -Matching Problem is NP-hard

José-Miguel Díaz-Báñez, Ruy Fabila-Monroy, José-Manuel Higes-López +3

Let $G$ be a complete edge-weighted graph on $n$ vertices. To each subset of vertices of $G$ assign the cost of the minimum spanning tree of the subset as its weight. Suppose that…

math.CO2024★ 1 cited

On the rectilinear crossing number of complete balanced multipartite graphs and layered graphs

Ruy Fabila-Monroy, Rosna Paul, Jenifer Viafara-Chanchi +1

A rectilinear drawing of a graph is a drawing of the graph in the plane in which the edges are drawn as straight-line segments. The rectilinear crossing number of a graph is the mi…

math.CO2024

On the Treewidth of Token and Johnson Graphs

Ruy Fabila-Monroy, Sergio Gerardo Gómez-Galicia, César Hernández-Cruz +1

Let $G$ be a graph on $n$ vertices and $1 \leq k \leq n$ a fixed integer. The \textit{ $k$ -token graph} of $G$ is the graph $F_{k} (G)$ whose vertex set consists of all $k$ -subsets of th…

cs.CG2023

A Note on the $k$ -colored Crossing Ratio of Dense Geometric Graphs

Ruy Fabila-Monroy

A \emph{geometric graph} is a graph whose vertex set is a set of points in general position in the plane, and its edges are straight line segments joining these points. We show tha…

math.CO2022★ 1 cited

Connected ( $C_{4}$ ,Diamond)-free Graphs Are Uniquely Reconstructible from Their Token Graphs

Ruy Fabila-Monroy, Ana Laura Trujillo-Negrete

A diamond is the graph that is obtained from removing an edge from the complete graph on $4$ vertices. A ( $C_{4}$ ,diamond)-free graph is a graph that does not contain a diamond or a…

math.CO2020★ 1 cited

On the Laplacian spectra of token graphs

C. Dalfó, F. Duque, R. Fabila-Monroy +4

We study the Laplacian spectrum of token graphs, also called symmetric powers of graphs. The $k$ -token graph $F_{k} (G)$ of a graph $G$ is the graph whose vertices are the $k$ -subsets…

cs.CG2020

Empty Rainbow Triangles in $k$ -colored Point Sets

Ruy Fabila-Monroy, Daniel Perz, Ana Laura Trujillo-Negrete

Let $S$ be a set of $n$ points in general position in the plane. Suppose that each point of $S$ has been assigned one of $k \geq 3$ possible colors and that there is the same number…

math.CO2020★ 9 cited

On the Connectivity of Token Graphs of Trees

Ruy Fabila-Monroy, Jesús Leaños, Ana Laura Trujillo-Negrete

Let $k$ and $n$ be integers such that $1 \leq k \leq n - 1$ , and let $G$ be a simple graph of order $n$ . The $k$ -token graph $F_{k} (G)$ of $G$ is the graph whose vertices are the $k$ -su…

cs.CG2020★ 1 cited

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 $n$ points in a convex domain in $R^{d}$ can be rounded to points on a grid of step size proportional to $1/n^{d+1+ε…

cs.CG2019

On the 2-colored crossing number

Oswin Aichholzer, Ruy Fabila-Monroy, Adrian Fuchs +4

Let $D$ be a straight-line drawing of a graph. The rectilinear 2-colored crossing number of $D$ is the minimum number of crossings between edges of the same color, taken over all p…

math.CO2019

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…

cs.CG2019

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…

cs.CG2018

On the Number of Order Types in Integer Grids of Small Size

Luis E. Caraballo, José-Miguel Díaz-Báñez, Ruy Fabila-Monroy +3

Let ${p_{1}, \dots, p_{n}}$ and ${q_{1}, \dots, q_{n}}$ be two sets of $n$ labeled points in general position in the plane. We say that these two point sets have the same order type if for…

cs.DM2018

Optimal Grid Drawings of Complete Multipartite Graphs and an Integer Variant of the Algebraic Connectivity

Ruy Fabila-Monroy, Carlos Hidalgo-Toscano, Clemens Huemer +2

How to draw the vertices of a complete multipartite graph $G$ on different points of a bounded $d$ -dimensional integer grid, such that the sum of squared distances between vertices…

math.CO2018★ 7 cited

The exact chromatic number of the convex segment disjointness graph

Ruy Fabila-Monroy, Jakob Jonsson, Pavel Valtr +1

Let $P$ be a set of $n$ points in strictly convex position in the plane. Let $D_{n}$ be the graph whose vertex set is the set of all line segments with endpoints in $P$ , where disjoi…

cs.CG2018

Colored ray configurations

Ruy Fabila-Monroy, Alfredo García, Ferran Hurtado +6

We 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 a…

cs.CG2017★ 9 cited

On balanced 4-holes in bichromatic point sets

S. Bereg, J. M. Díaz-Báñez, R. Fabila-Monroy +5

Let $S = R \cup B$ be a point set in the plane in general position such that each of its elements is colored either red or blue, where $R$ and $B$ denote the points colored red and th…

math.CO2017

Non-crossing Monotone Paths and Binary Trees in Edge-ordered Complete Geometric Graphs

Frank Duque, Ruy Fabila-Monroy, Carlos Hidalgo-Toscano +1

An edge-ordered graph is a graph with a total ordering of its edges. A path $P = v_{1} v_{2} \dots v_{k}$ in an edge-ordered graph is called increasing if $(v_{i} v_{i + 1}) > (v_{i + 1} v_{i + 2})$ …

cs.CG2016★ 1 cited

Updating the Number of Crossings in Rectilinear Drawings of the Complete Graph

Frank Duque, Ruy Fabila-Monroy

Let $S$ be a set of $n$ points in general position in the plane. Join every pair of points in $S$ with a straight line segment. Let $cr (S)$ be number of pairs of these e…

cs.CG2016

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.…

cs.CG2015

Balanced Islands in Two Colored Point Sets in the Plane

Oswin Aichholzer, Nieves Atienza, Ruy Fabila-Monroy +5

Let $S$ be a set of $n$ points in general position in the plane, $r$ of which are red and $b$ of which are blue. In this paper we prove that there exist: for every $α\in \left [ 0,…

math.CO2015★ 32 cited

Regularity and Planarity of Token Graphs

Walter Carballosa, Ruy Fabila-Monroy, Jesús Leaños +1

Let $G = (V, E)$ be a graph of order $n$ and let $1 \leq k < n$ be an integer. The $k$ -token graph of $G$ is the graph whose vertices are all the $k$ -subsets of $V$ , two of which are ad…