Optimal Strategies for Generalized Saturation Games

The authors study a game version of the generalized graph Turán problem, where two players, Max and Mini, alternately claim unclaimed edges of the complete graph Kn such that the graph of the claimed edges must remain F-free throughout the game. The H-score of the game is the number of copies of H in the final graph, and the goal is to maximize or minimize this score, respectively.