Herbert Edelsbrunner

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20232026

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math.CO2024

On Spheres with $k$ Points Inside

Herbert Edelsbrunner, Alexey Garber, Morteza Saghafian

We generalize the classic definition of Delaunay triangulation and prove that for a locally finite and coarsely dense generic point set, $A \subseteq R^{d}$ , the $d$ -simplic…

math.CO2023

Maximum Betti numbers of Čech complexes

Herbert Edelsbrunner, János Pach

The Upper Bound Theorem for convex polytopes implies that the $p$ -th Betti number of the Čech complex of any set of $N$ points in $R^{d}$ and any radius satisfies $β_{p} = O(…

math.CO2023

Order-2 Delaunay Triangulations Optimize Angles

Herbert Edelsbrunner, Alexey Garber, Morteza Saghafian

The local angle property of the (order- $1$ ) Delaunay triangulations of a generic set in $R^{2}$ asserts that the sum of two angles opposite a common edge is less than $π$ . T…

On Spheres with k Points Inside

Maximum Betti numbers of Čech complexes

Order-2 Delaunay Triangulations Optimize Angles

On Spheres with $k$ Points Inside