2 problems

Hamiltonicity conjecture. The graph $G(L(P))$ has a Hamiltonian cycle.

Let $\mathcal{P}(m,n)$ be the partial permutohedron and let $\mathcal{B}_m$ be the Boolean lattice of subsets of $[m]$. For a chain in $\mathcal{B}_m$, the difference between its l…