Matchings of quadratic size extend to long cycles in hypercubes

Ruskey and Savage in 1993 asked whether every matching in a hypercube can beextended to a Hamiltonian cycle. A positive answer is known for perfectmatchings, but the general case has been resolved only for matchings of linearsize. In this paper we show that there is a quadratic function $q(n)$ such thatevery matching in the $n$-dimensional hypercube of size at most $q(n)$ may beextended to a cycle which covers at least $\frac34$ of the vertices

Matchings of quadratic size extend to long cycles in hypercubes

Ruskey and Savage in 1993 asked whether every matching in a hypercube can be extended to a Hamiltonian cycle. A positive answer is known for perfect matchings, but the general case has been resolved only for matchings of linear size. In this paper we show that there is a quadratic function $q(n)$ such that every matching in the $n$-dimensional hypercube of size at most $q(n)$ may be extended to a cycle which covers at least $\frac34$ of the vertices