The Peripatetic Salesman and Some Related Unsolved Problems

Abstract

Some generalizations of the traveling salesman prob~em are suggested, leading to problems in which we seek to minimize the summed weight of two or more line-disjoint hamiltonian cycles. A number of seemingly open questions extending the concept of ha-miltonian graphs are raised. Finally, pursuing the Held-Karp approach for solving symmetric traveling salesman problems, an extension of the minimum spanning tree problem is briefly discussed.