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...

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?