6 problems

Let $\mathcal{M}_n$ be the set of the labelled perfect matchings under consideration, and let $\preceq$ be the preorder on this set. A switch is the local transformation defined ea…

Minimality criterion conjecture. The graph $G'$ is a minimal graph if and only if it does not contain such a chain of 3-cycles.

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.

Large-grid conjecture. The forthcoming results apply for grid graphs such that