3 problems

Let $\mathsf{N}$ be a double-edge normal factor graph (DE-NFG). For each integer $M\geq 1$, let $Z_{\mathrm{B},M}(\mathsf{N})$ denote the degree-$M$ Bethe partition function, defin…

Graph-cover characterization conjecture. It holds that

A pseudo $2$-factor isomorphic graph is a graph admitting a $2$-factor such that the parity of the number of cycles is the same for all its $2$-factors. A graph is cubic if every v…