2 problems

For each integer $n\geq 1$, let $\mathsf{S}_n(-1)=\{P_G(-1):G\text{ is a simple graph on }n\text{ vertices}\}$. Since $|P_G(-1)|$ counts acyclic orientations of $G$, the spectrum c…

Let $G$ be an $n$-vertex graph, and let $\alpha,\alpha”\in\operatorname{Acyc}(G)$ be double-flip equivalent, meaning that they can be connected by a sequence of allowed double-flip…