6 problems

Maximum-degree phase-transition conjecture. There is a threshold $\alpha_1$ on the average degree such that below it an optimal graph has a vertex of degree $\Omega(n)$, whereas ab…

Leaf-density phase-transition conjecture. There is a threshold $\alpha_0$ on the average degree such that below it all optimal graphs have a positive proportion of leaves, whereas…

Convex lower-bound conjecture. For all $x$,

Conditional local-move existence conjecture. For every integer $n\geq 3$, there exists a conditional local move on $\Pi_n$ such that:

Hexagon conditional local-move conjecture. There is a hexagon conditional local move of the displayed form, with the conjectural conductance formulas described in the paper, that p…

Local-move completeness conjecture. Any two electrically equivalent graphs associated to rnpds are connected by the local moves stated in this section.