7 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 $G=(V,E)$ 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…

Asymptotic prevalence conjecture. Almost all transitive permutation groups have exponential graph growth, in the sense that

Block-kernel characterization. The group $L$ has exponential graph growth if and only if it admits a proper block $B$ such that

Polynomial-growth product-structure conjecture. There exist functions $g\colon\mathbb{R}\times\mathbb{N}\to\mathbb{N}$ and $h\colon\mathbb{R}\times\mathbb{N}\to\mathbb{R}$ such tha…

Linear-growth product-structure conjecture. There exist functions $g\colon\mathbb{R}\to\mathbb{N}$ and $h\colon\mathbb{R}\to\mathbb{R}$ such that for any $c\geqslant 1$, every grap…

Monotonicity conjecture. The maximal possible growth rate of a $k$-regular dual graph of a Dirichlet tiling is monotone decreasing in the dimension, as long as $k>d$; for larger…