Tours for the traveling salesman

摘要

Two characterizations are given for the set of all tours for the n×n traveling salesman problem. New insights about tours are obtained by viewing them as discrete points which are uniformly distributed on a tours. When n is a prime number, the algebraic structure of tours yields combinatorial results which give significant properties to the geometric model on the tours. When a distance matrix is changed by adding or deleting a row and column of zeros, then under certain conditions, optimal tours for the matrices are related.