Bounds and constructions for n-e.c. tournaments

Few families of tournaments satisfying the n-e.c.\ adjacency property are known. We supply a new random construction for generating infinite families of vertex-transitive n-e.c.\ tournaments by considering circulant tournaments. Switching is used to generate exponentially many n-e.c.\ tournaments of certain orders. With aid of a computer search, we demonstrate that there is a unique minimum order 3-e.c.\ tournament of order 19, and there are no 3-e.c.\ tournaments of orders 20, 21, and 22.