Nomadic decompositions of bidirected complete graphs

Abstract: We use to denote the bidirected complete graph on n vertices. A nomadic Hamiltonian decomposition of is a Hamiltonian decomposition, with the additional property that “nomads” walk along the Hamiltonian cycles (moving one vertex per time step) without colliding. A nomadic near-Hamiltonian decomposition is defined similarly, except that the cycles in the decomposition have length , rather than length n. Bondy asked whether these decompositions of exist for all n. We show that admits a nomadic near-Hamiltonian decomposition when . [Copyright &y& Elsevier]