Towards a Classification of Hamiltonian Cycles in the 6-Cube

Abstract

In this paper, we consider the problem of classifying Hamiltonian cycles in a binary hypercube. Previous work proposed a classification of these cycles using the edge representation, and presented it for dimension 4. We classify cycles in two further dimensions using a reduction to propositional SAT. Our proposed algorithm starts with an over-approximation of the set of equivalence classes, which is then refined using queries to a SAT-solver to remove spurious cycles. Our method performs up to three orders of magnitude faster than an enumeration with symmetry breaking in the 5-cube.