Kaiser et al.'s prism-toughness conjecture

Let $G$ be a simple finite graph. The prism over $G$ is the Cartesian product

$$G\mathbin{\Box}K_2.$$

A graph is prism-hamiltonian when its prism is hamiltonian. Call $G$ $t$-tough if $|S|\geq t\,c(G-S)$ for every $S\subseteq V(G)$ with $c(G-S)\geq 2$.

Kaiser et al.'s prism-toughness conjecture. There exists a constant $t_1$ such that the prism over any $t_1$-tough graph is hamiltonian.

Hamiltonian paths imply prism-hamiltonicity, which implies the existence of a spanning $2$-walk, but neither implication reverses in general. The conjecture asks whether a universal toughness threshold guarantees prism-hamiltonicity and remains open.