Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Let n be a positive integer. A tournament is called n-existentially closed (or n-e.c.) if for every subset S of n vertices and for every subset T of S, there is a vertex x@?S which is directed toward every vertex in T and directed away from every vertex in S@?T.  prove that there is a 2-e.c. tournament with k vertices if and only if k>=7 and k 8, and give explicit examples for all such orders k.  also give a replication operation which preserves the 2-e.c. property.
['Anthony Bonato', 'Kathie Cameron']
I am writing a research paper on a idea On an adjacency property of almost all tournaments
[{"from": "human", "value": "I am writing a research paper on a idea On an adjacency property of almost all tournaments"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Let n be a positive integer. A tournament is called n-existentially closed (or n-e.c.) if for every subset S of n vertices and for every subset T of S, there is a vertex x@?S which is directed toward every vertex in T and directed away from every vertex in S@?T.  prove that there is a 2-e.c. tournament with k vertices if and only if k>=7 and k 8, and give explicit examples for all such orders k.  also give a replication operation which preserves the 2-e.c. property."}]