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arXiv · 2608.20010

Graphs with connectivity $3/4 - \varepsilon$ are globally synchronizing

Saba Lepsveridze·Sam Zhang
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Abstract

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 minimum degree at least $(3/4-η)n$ has no local minima of the Kuramoto energy other than the fully synchronized states. This strictly improves the previous $3/4$ upper bound and refutes a conjecture of Bandeira, Kireeva, Maillard, and Rödder.

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Saba Lepsveridze, Sam Zhang. 2026-08-20. Graphs with connectivity $3/4 - \varepsilon$ are globally synchronizing. https://arxiv.org/abs/2608.20010

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