Hamiltonian Cycles with Prescribed Edges in Hypercubes

Given a set P of at most 2n-3 prescribed edges (n≥2), the n-dimensional hypercube Qn contains a Hamiltonian cycle passing through all edges of P iff the subgraph induced by P consists of pairwise vertex-disjoint paths. This answers a question of Caha and Koubek, who showed that for any n≥3 there are 2n-2 edges of Qn not contained in any Hamiltonian cycle, but that still satisfy the above condition.