Nomadic decompositions of bidirected complete graphs

We use K n to denote the bidirected complete graph on n vertices. A nomadic Hamiltonian decomposition of K n 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 n - 1, rather than length n. J.A. Bondy asked whether these decompositions of K n exist for all n. We show that K n admits a nomadic near-Hamiltonian decomposition when n 2 mod 4.

• Type: Journal
• Year: 2008
• Where: DM
• Authors: Daniel W. Cranston
• Keywords: DM 2008, Hamiltonian Decomposition, Nomadic Hamiltonian Decomposition, Nomadic Near-Hamiltonian Decomposition