Guillermo Pineda-Villavicencio

activity

20172025

collaborators

19 papers

math.CO2025

A lower bound theorem for $d$ -polytopes with at most $3 d - 1$ vertices

Guillermo Pineda-Villavicencio, Jie Wang

We prove a lower bound theorem for the number of $k$ -faces ( $1 \leq k \leq d - 2$ ) in a $d$ -dimensional polytope $P$ (or $d$ -polytope) with up to $3 d - 1$ vertices. Previous lower bound th…

math.CO2025

A refined lower bound theorem for $d$ -polytopes with at most $2 d$ vertices

Guillermo Pineda-Villavicencio, Jie Wang, David Yost

In 1967, Grünbaum conjectured that the function $ϕ_{k} (d + s, d) := (k + 1 d + 1) + (k + 1 d) - (k + 1 d + 1 - s), for 2 \leq s \leq d$ provides the minimum number of $k$ -…

math.CO2024

A lower bound theorem for $d$ -polytopes with $2 d + 2$ vertices

Guillermo Pineda-Villavicencio, Aholiab Tritama, Jie Wang +1

We establish a lower bound theorem for the number of $k$ -faces ( $1 \leq k \leq d - 2$ ) in a $d$ -dimensional polytope $P$ (abbreviated as a $d$ -polytope) with $2 d + 2$ vertices, extending t…

math.CO2024

Polytopes with low excess degree

Guillermo Pineda-Villavicencio, Jie Wang, David Yost

We study the existence and structure of $d$ -polytopes for which the number $f_{1}$ of edges is small compared to the number $f_{0}$ of vertices. Our results are more elegantly expresse…

math.CO2022

Edge connectivity of simplicial polytopes

Vincent Pilaud, Guillermo Pineda-Villavicencio, Julien Ugon

We show that the graph of a simplicial polytope of dimension $d \geq 3$ has no nontrivial minimum edge cut with fewer than $d (d + 1) /2$ edges, hence the graph is $min {δ, d (d + 1) /2}$ …

math.CO2022

Cycle space of graphs of polytopes

Guillermo Pineda-Villavicencio

It is folklore that the cycle space of graphs of polytopes is generated by the cycles bounding the 2-faces. We provide a proof of this result that bypass homological arguments, whi…