R. Fabila-Monroy

activity

20092026

most citedToken Graphs

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

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20 papers · 1 filter

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…

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…

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…

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…

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…

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…

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 $(v_{i} v_{i + 1}) > (v_{i + 1} v_{i + 2})$ …

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…

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.CO2012

New results on the coarseness of bicolored point sets

J. M. Díaz-Báñez, R. Fabila-Monroy, P. Pérez-Lantero +1

Let $S$ be a 2-colored (red and blue) set of $n$ points in the plane. A subset $I$ of $S$ is an island if there exits a convex set $C$ such that $I = C \cap S$ . The discrepancy of an…

math.CO2012★ 1 cited

The Erdős-Sós Conjecture for Geometric Graphs

Luis F. Barba, Ruy Fabila-Monroy, Dolores Lara +4

Let $f (n, k)$ be the minimum number of edges that must be removed from some complete geometric graph $G$ on $n$ points, so that there exists a tree on $k$ vertices that is no longer…

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…

math.CO2011★ 1 cited

Colouring the Triangles Determined by a Point Set

Ruy Fabila-Monroy, David R. Wood

Let P be a set of n points in general position in the plane. We study the chromatic number of the intersection graph of the open triangles determined by P. It is known that this ch…

math.CO2011★ 1 cited

Decompositions of Complete Multipartite Graphs into Complete Graphs

Ruy Fabila-Monroy, David R. Wood

Let $k \geq ℓ \geq 1$ and $n \geq 1$ be integers. Let $G (k, n)$ be the complete $k$ -partite graph with $n$ vertices in each colour class. An $ℓ$ -decomposition of $G (k, n)$ is a set…

math.CO2011

The chromatic number of the convex segment disjointness graph

Ruy Fabila-Monroy, David R. Wood

Let $P$ be a set of $n$ points in general and 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 dis…

math.CO2011

Rooted $K_{4}$ -Minors

Ruy Fabila-Monroy, David R. Wood

Let $a, b, c, d$ be four vertices in a graph $G$ . A \emph{ $K_{4}$ -minor rooted} at $a, b, c, d$ consists of four pairwise-disjoint pairwise-adjacent connected subgraphs of $G$ , respectivel…

math.CO2009★ 65 cited

Token Graphs

Ruy Fabila-Monroy, David Flores-Peñaloza, Clemens Huemer +3

For a graph $G$ and integer $k \geq 1$ , we define the token graph $F_{k} (G)$ to be the graph with vertex set all $k$ -subsets of $V (G)$ , where two vertices are adjacent in $F_{k} (G)$ when…

Blow-ups of order types of positive density

Domination number of Token Graphs

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

On the Treewidth of Token and Johnson Graphs

Connected (C4​,Diamond)-free Graphs Are Uniquely Reconstructible from Their Token Graphs

On the Laplacian spectra of token graphs

On the Connectivity of Token Graphs of Trees

An Ongoing Project to Improve the Rectilinear and the Pseudolinear Crossing Constants

The exact chromatic number of the convex segment disjointness graph

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

Regularity and Planarity of Token Graphs

(n,m)-Fold Covers of Spheres

New results on the coarseness of bicolored point sets

The Erdős-Sós Conjecture for Geometric Graphs

On the Connectedness and Diameter of a Geometric Johnson Graph

Colouring the Triangles Determined by a Point Set

Decompositions of Complete Multipartite Graphs into Complete Graphs

The chromatic number of the convex segment disjointness graph

Rooted K4​-Minors

Token Graphs

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

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

Rooted $K_{4}$ -Minors