M. Kahle

activity

20062026

most citedRandom geometric complexes

172 citations · 377 across the 33 of their papers we have counts for

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19 papers · 1 filter

math.CO2024

Maximum Persistent Betti Numbers of Čech Complexes

Herbert Edelsbrunner, Matthew Kahle, Shu Kanazawa

This note proves that only a linear number of holes in a Čech complex of $n$ points in $R^{d}$ can persist over an interval of constant length. Specifically, for any fixed d…

math.CO2022

Maximal persistence in random clique complexes

Ayat Ababneh, Matthew Kahle

We study the persistent homology of an Erdős--Rényi random clique complex filtration on $n$ vertices. Here, each edge $e$ appears at a time $p_{e} \in [0, 1]$ chosen uniform randomly…

math.CO2022

On the clique number of noisy random geometric graphs

Matthew Kahle, Minghao Tian, Yusu Wang

Let $G_{n}$ be a random geometric graph, and then for $q, p \in [0, 1)$ we construct a " $(q, p)$ -perturbed noisy random geometric graph" $G_{n}^{q, p}$ where each existing edge in $G_{n}$ is…

math.CO2022★ 2 cited

Facets of Random Symmetric Edge Polytopes, Degree Sequences, and Clustering

Benjamin Braun, Kaitlin Bruegge, Matthew Kahle

Symmetric edge polytopes are lattice polytopes associated with finite simple graphs that are of interest in both theory and applications. We investigate the facet structure of symm…

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.CO2020

Topology of random 2-dimensional cubical complexes

Matthew Kahle, Elliot Paquette, Érika Roldán

We study a natural model of random 2-dimensional cubical complex which is a subcomplex of an n-dimensional cube, and where every possible square $2$ -face is included independently…