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Given a set P of at most 2n − 4 prescribed edges (n 5) and vertices u and v whose mutual distance is odd, the n-dimensional hypercube Q n contains a hamiltonian path between u and v passing through all edges of P iff the subgraph induced by P consists of pairwise vertex-disjoint paths, none of them having u or v as internal vertices or both of them as endvertices. This resolves a problem of Caha and Koubek who showed that for any n 3 there exist vertices u, v and 2n − 3 edges of Q n not contained in any hamiltonian path between u and v, but still satisfying the condition above. The proof of the main theorem is based on an inductive construction whose basis for n = 5 was verified by a computer search. Classical results on hamiltonian edge-fault tolerance of hypercubes are obtained as a corollary.

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