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Bounds and constructions for $$n$$-e.c. tournaments. (English) Zbl 1317.05160
Summary: 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.

##### MSC:
 05C75 Structural characterization of families of graphs 05C85 Graph algorithms (graph-theoretic aspects) 05C80 Random graphs (graph-theoretic aspects)