Ramsey graph game

Ramsey graph game --- рамсеевская игра на графах.

The board of the game is the complete graph [math]\displaystyle{ K_{s} }[/math] with [math]\displaystyle{ s }[/math] vertices. The players alternately occupy the edges of [math]\displaystyle{ K_{s} }[/math], and that player wins who first occupies all the [math]\displaystyle{ \left(\begin{array}{c} n \\ 2\end{array}\right) }[/math] edges of some complete subgraph [math]\displaystyle{ K_{n} }[/math]. The Ramsey Graph Game is denoted by [math]\displaystyle{ R(s,n) }[/math].