According to Bennett’s model of cytogenetics the spatial order in haploid chromosome complements is based on a similarity relation which gives rise to a multigraph G which is the edge disjoint union of two of its subgraphs G1 and G2. If the number of chromosomes is even, the order of the chromosomes is determined by a Hamiltonian circuit of G which is alternating in the edges of G1 and G2. However, contrary to assumptions made by biologists, such an Hamiltonian circuit does not exist in general. This paper studies modifications of the underlying similarity relation (which are in agreement with the biological context) which guarantee that, under certain conditions, Hamiltonian circuits of the mentioned type do always exist, i.e. the rules in Bennett’s model become consistent.
