2 problems

Suppose $G=(V,E)$ is a finite, connected, simple graph. For $x,y\in V$, let $\mathscr{S}(x,y)$ be the set of self-avoiding walks from $x$ to $y$, and let $\mathscr{S}(u_i,v_j)$ den…

The bunkbed conjecture. For every such $G$, the following three inequalities hold: