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.
Ali et al. (Sat,) studied this question.