连通度为$3/4 - \varepsilon$的图是全局同步的
Graphs with connectivity $3/4 - \varepsilon$ are globally synchronizing
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中文总结 AI 辅助
本研究针对有限图上的Kuramoto模型同步问题，证明最小度满足$(3/4-\eta)n$的有限简单图无额外局部极小值，改进了此前3/4的上界并否定了相关猜想。
中文摘要 AI 辅助
我们研究有限图上Kuramoto模型（仓本模型）的同步现象。证明存在绝对常数$\eta>0$，使得每个具有$n$个顶点、最小度至少为$(3/4-\eta)n$的有限简单图$G$，其Kuramoto能量除完全同步态外不存在局部极小值。该结果严格改进了此前的$3/4$上界，并否定了Bandeira、Kireeva、Maillard与Rödder的一个猜想。
英文摘要
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.
