Problem

A tournament is a digraph in which there is exactly one edge between every two vertices.a....

A tournament is a digraph in which there is exactly one edge between every two vertices.

a. How many edges does a tournament have?



b. How many different tournaments of n edges can be created?



c. Can each tournament be topologically sorted?


d. How many minimal vertices can a tournament have?



e. A transitive tournament is a tournament that has edge(vw) if it has edge(vu) and edge(uw). Can such a tournament have a cycle?

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