On Extension of Matchings to Hamiltonian Cycles in 6-Cubes

The problem initially raised by Ruskey and Savage: whether every matching in an [Formula: see text]-dimensional hypercube [Formula: see text] with [Formula: see text] can be extended to form a Hamiltonian cycle. Fink addressed Kreweras’ conjecture by proving that all perfect matchings in [Formula: see text] are extendable to Hamiltonian cycles, and also demonstrated that this extension property holds for all matchings when [Formula: see text]. Later, Wang and Zhao expanded the result by showing that every matching in [Formula: see text] can be extended to the Hamiltonian cycle. In this work, we further contribute to this area by proving that every matching consisting of up to 20 edges in the 6-dimensional hypercube [Formula: see text] can be extended to a Hamiltonian cycle.