ON THE STRONG PATH CONNECTIVITY OF A TOURNAMENT

B. Alspach has shown that an irregular tournament T=(V,A) is arc-pancyclic. The purpose of this paper is to give a sufficient condition by which it can be verified that when p≥7, for any arc (v, v_0), in a tournament T there is a path of length k from v_0 to v. And when p≥10, in T also there is a path of length k from v to v_0 (k=3,4,…p-1), where p=丨V丨 is the number of vertices of T. In this sense, this article gives a sufficient condition on strong path connectivity of a tournament and hence it generalizes Alspach's result.