5 problems

The sharp alpha-metric hyperbolicity conjecture. The right upper bound for the hyperbolicity of an $\alpha_i$-metric graph might be

A graph $G$ is $(\lambda,\mu)$-bow metric if, whenever shortest paths $P(u,w)$ and $P(v,x)$ share a common shortest subpath $P(v,w)$ of length more than $\lambda$, one has … A grap…

Hyperbolic graph conjecture. Although for $n\geq 4$ the graph ${\mathcal{P}\mathcal{G}}_n$ does not have the property that every exponentially growing automorphism acts on it with…

Let $\operatorname{FPP}_1$ and $\operatorname{FPP}_\lambda$ be competing first passage percolation processes, with respective passage-rate parameters $1$ and $\lambda$, started fro…

Forbidden-subgraph conjecture. A $6$-chordal graph is $\frac{1}{2}$-hyperbolic if and only if it does not contain any of the ten special graphs $G_1,G_2,G_3,C_4,C_6,H_i$,…