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Curvature-Distortion Numbers of Graphs: Prescribed Lin--Lu--Yau Curvature Lower Bounds
We study an optimization problem for weighted Lin--Lu--Yau curvature. Given a graph $G=(V,E)$ and a prescribed lower curvature bound $k\ge0$, we ask for the smallest multiplicative distortion \[ \Dist(w):=\frac{\sup_{e\in E}w_e}{\inf_{e\in E}w_e} \] of the edge weights needed to make every edge have
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