Francisco Martinez-Figueroa

activity

20192022

collaborators

4 papers

math.CO2022

Topology and chromatic number of random $ε$ -distance graphs on spheres

Francisco Martinez-Figueroa

Given $0 < α \leq π$ , $ε > 0$ and $n$ , we define random graphs on the $d$ -dimensional sphere by drawing $n$ i.i.d. uniform random points for the vertices, and edges $u \sim v$ whenever…

math.CO2021

Generalized Borsuk Graphs

Francisco Martinez-Figueroa

Given a finite group $G$ acting freely on a compact metric space $M$ , and $ε > 0$ , we define the $G$ -Borsuk graph on $M$ by drawing edges $x \sim y$ whenever there is a non-identity $…

math.CO2020

A square-grid coloring problem

Matthew Kahle, Francisco Martinez-Figueroa, Alexander Soifer

Suppose that $n \geq 2$ , and we wish to plant $k$ different types of trees in the squares of an $n \times n$ square grid. We can have as many of each type as we want. The only rule…

math.CO2019

The chromatic number of random Borsuk graphs

Matthew Kahle, Francisco Martinez-Figueroa

We study a model of random graph where vertices are $n$ i.i.d. uniform random points on the unit sphere $S^{d}$ in $R^{d + 1}$ , and a pair of vertices is connected if the Eucl…

Topology and chromatic number of random ε-distance graphs on spheres

Generalized Borsuk Graphs

A square-grid coloring problem

The chromatic number of random Borsuk graphs

Topology and chromatic number of random $ε$ -distance graphs on spheres