In graph theory, how do you obtain the number of tournaments with 'N' nodes? Define a transitive tournament. Define a sub-tournament. What is the lower bound on the size of the maximal transitive sub-tournament for each tournament?

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The aim is to find an upper bound for the minimum number of nodes in a maximal transitive sub-tournament.

A transitive tournament is one where any three nodes can be arranged in a way that satisfies the transitive property.
A sub-tournament is an induced graph on a subset of nodes from the original tournament.
Every tournament with N nodes contains a transitive sub-tournament of size 2 (a directed edge).
The goal is to find the maximal transitive sub-tournament with the minimum number of nodes.
The aim is to upper bound the minimum number of nodes in the maximal transitive sub-tournament.