4 problems

Boesch's conjecture. Each uniformly most reliable graph in $\mathcal{C}_{n,m}$ is a $0$-element in $\mathcal{C}_{n,m}$.

Let $FCG_{n,c}$ denote the fair cake-cutting graph with parameters $n$ and $c$. A graph is uniformly most reliable for fixed order $n$ and size $m$ if its reliability polynomial is…

Mesh-network bondage conjecture. For $m\geqslant 5$,

Edge-connectivity UBB conjecture. If