Gerardo L. Maldonado

activity

20212026

collaborators

5 papers

math.CO2026

Disconnected graphs and extremal bounds for realizable distance orders

Gerardo L. Maldonado, Leonardo Martínez-Sandoval, Miguel Raggi +1

Let $G$ be a graph together with a total order $≺$ on its edges. We say that $≺$ is realizable in $R^{d}$ if there is a placement of the vertices of $G$ in $\mathbb{…

math.DS2026

Extinction thresholds in a graph-based model of HIV infection dynamics

Manuel A. Espinosa-García, Ana Paulina Figueroa, Julián A. Fresán-Figueroa +2

We study a graph-based cellular automaton for HIV infection dynamics in lymph-node networks, originally introduced by Mukwembi. Each vertex represents a cell site that may be healt…

math.CO2024

On the orthogonal Grünbaum partition problem in dimension three

Gerardo L. Maldonado, Edgardo Roldán-Pensado

Grünbaum's equipartition problem asked if for any measure $μ$ on $R^{d}$ there are always $d$ hyperplanes which divide $R^{d}$ into $2^{d}$ $μ$ -equal parts. This proble…

math.CO2023

Total orders realizable as the distances between two sets of points

Gerardo L. Maldonado, Miguel Raggi Pérez, Edgardo Roldán-Pensado

In this note we give a negative answer to a question proposed by Almendra-Hernández and Martínez-Sandoval. Let $n \leq m$ be positive integers and let $X$ and $Y$ be sets of sizes $n…

cs.CG2021

Dissecting the square into seven or nine congruent parts

Gerardo L. Maldonado, Edgardo Roldán-Pensado

We give a computer-based proof of the following fact: If a square is divided into seven or nine convex polygons, congruent among themselves, then the tiles are rectangles.