Saba Lepsveridze

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20232026

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4 papers · 1 filter

math.CO2026

Graphs with connectivity $3/4 - ε$ are globally synchronizing

Saba Lepsveridze, Sam Zhang

We study synchronization in the Kuramoto model on finite graphs. We prove that there is an absolute constant $η > 0$ such that every finite simple graph $G$ on $n$ vertices with mini…

math.CO2026

Uniform Geodesic Drawings of Graphs

Saba Lepsveridze, Oriol Solé-Pi

We study crossing numbers of dense graph drawings whose vertices are uniformly distributed either on the unit sphere or in a compact convex planar domain. We prove a sharp inequali…

math.CO2023

Uniacute Spherical Codes

Saba Lepsveridze, Aleksandre Saatashvili, Yufei Zhao

A spherical $L$ -code, where $L \subseteq [- 1, \infty)$ , consists of unit vectors in $R^{d}$ whose pairwise inner products are contained in $L$ . Determining the maximum cardin…

math.CO2023

Size of the largest sum-free subset of $[n]^{3}$ and $[n]^{4}$

Saba Lepsveridze, Yihang Sun

We determine the density of the largest sum-free subset of the lattice cube ${1, 2, \dots, n}^{d}$ for $d = 3$ and $d = 4$ . This solves a conjecture of Cameron and Aydinian in dime…

Graphs with connectivity 3/4−ε are globally synchronizing

Uniform Geodesic Drawings of Graphs

Uniacute Spherical Codes

Size of the largest sum-free subset of [n]3 and [n]4

Graphs with connectivity $3/4 - ε$ are globally synchronizing

Size of the largest sum-free subset of $[n]^{3}$ and $[n]^{4}$