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Ruskey and Savage asked the following question: Does every matching of$Q_{n}$ for $n\geq2$ extend to a Hamiltonian cycle of $Q_{n}$? J. Fink showedthat the question is true for every perfect matching, and solved the Kreweras'conjecture. In this paper we consider the question in hypercubes with faultyedges. We show that every matching $M$ of at most $2n-1$ edges can be extendedto a Hamiltonian cycle of $Q_{n}$ for $n\geq2$. Moreover, we can prove thatwhen $n\geq4$ and $M$ is nonempty this result still holds even if $Q_{n}$ hasat most $n-1-\lceil\frac{|M|}{2}\rceil$ faulty edges with one exception.

Prescribed matchings extend to Hamiltonian cycles in hypercubes with faulty edges