6 problems

Let $G=(V,E)$ be a graph with non-negative Ollivier–Ricci curvature and degrees bounded by $d<\infty$. Write $B(x,r)$ for the ball of radius $r$ centred at $x$, let…

Let $G$ be a transitive graph with non-negative Ollivier--Ricci curvature. Recall that two metric spaces are quasi-isometric if they are equivalent up to multiplicative and additiv…

Let $G=(V,E)$ be a graph, let $dgeq 1$, and suppose that $G$ has non-negative Ollivier--Ricci curvature and degrees bounded by $d$. Write $B(x,r)$ for the ball of radius $r$ center…

Let $\mathcal{M}_{d}$ denote the maximum number of vertices of a connected $d$-regular graph with positive Lin–Lu–Yau curvature. For even degree, write $d\in2\mathbb{N}$. Extremal-…

Let $G$ be a connected $d$-regular graph, and let $\operatorname{Ric}(G)$ denote its Ollivier-Ricci curvature. Positive-curvature conjecture for regular graphs. Every $d$-regular g…

Bakry–Émery curvature Bonnet–Myers conjecture. One has