ON THE STRONG PATH CONNECTIVITY OF A TOURNAMENT

<正> 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, v0）, in a tournament T there is a path of length k from v0 to v. And when p≥10, in T also there is a path of length k from v to v0 （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.