3 problems

Amicability conjecture. For every network $G$ and every pair of distinct vertices $v$ and $w$, the pair $\{v,w\}$ is amicable in $G$.

Multivariate Brown–Colbourn conjecture. If $|q_e|>1$ for all $e$, then

Let $G=(V,E)$ be a connected graph, and let $\mathrm{Rel}(G;q)$ denote its all-terminal reliability polynomial in the edge-failure probability $q$. A complex number $z$ is an all-t…