QUASI-RANDOM TOURNAMENTS

We introduce a large class of tournament properties, all of which are shared by almost all random tournaments. These properties, which we term "quasi-random", have the property that tournaments possessing any one of the properties must of necessity possess them all. In contrast to random tournaments, however, it is often very easy to verify that a particular family of tournaments satisfies one of the quasi-random properties, thereby giving explicit tournaments with "random-like" behavior. This paper continues an approach initiated in several earlier papers of the authors where analogous results for graphs (with R.M. Wilson) and hypergraphs are proved.