11 problems

The bunkbed conjecture for transitive tournaments. The statement

Let $G=(V,E)$ be an undirected graph, and let $(V^-,E^-)$ and $(V^+,E^+)$ be two copies of $G$. For each $v\in V$, write $v^-$ and $v^+$ for its copies, and form the bunkbed graph…

Let $G$ be a graph, and let $BB(G)$ be its bunkbed graph with two layers, whose corresponding vertices are denoted $x^-$ and $x^+$ for $x obreaktext{ in } obreak V(G)$. Let … be a…

Let $D$ be a simple digraph. Construct $\widetilde{D}$ by adding both directed vertical edges $v^{(0)}v^{(1)}$ and $v^{(1)}v^{(0)}$ for every $v\in V(D)$, and let $E_8$ select a su…

Let $\mathcal{H}$ be a hypergraph and let $T\subseteq V(\mathcal{H})$ be a set of posts. In the conditioned model $E_4^T(\widetilde{\mathcal{H}})$, precisely one of the two copies…

Let $G=(V,E)$ be a finite connected graph and let $T\subset V$. The bunkbed graph $G_T$ has vertex set $V\times\{0,1\}$, two horizontal copies of every edge of $G$, and a vertical…

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

Directed Bunkbed conjecture. For every $u,v\in V(G)$,

Hypergraph Bunkbed conjecture. For every $u,v\in V(G)$,

Two-color Bunkbed conjecture. For every $u,v\in V(G)$,

Generalized Bunkbed conjecture. For every $u,v\in V(G)$,