On the cycle structure of in-tournaments.
Meike Tewes, Lutz Volkmann · 1998
An in-tournament is an oriented graph such that the in-neighborhood of every vertex induces a tournament. Therefore, in-tournaments are a generalization of local tournaments where, for every vertex, the set of inneighbors as well as the set of out-neighbors induce a tournament. While local tournaments have been intensively studied very little is known about in-tournaments. It is the purpose of this paper to give more information about in-tournaments where we will focus mainly on the cycle structure of these digraphs. We will investigate the extendability of cycles and the influence of the minimum indegree on the cycle structure. In particular, we show that every strong in-tournament of order n with minimum indegree at least ~ is pancyclic. 1