Generalized saturation game
<|reference_start|>Generalized saturation game: We study the following game version of the generalized graph Tur\'an problem. For two fixed graphs F and H, two players, Max and Mini, alternately claim unclaimed edges of the complete graph Kn such that the graph G of the claimed edges must remain F-free throughout the game. The game ends when no further edges can be claimed, i.e. when G becomes F-saturated. The H-score of the game is the number of copies of H in G. Max aims to maximize the H-score, while Mini wants to minimize it. The H-score of the game when both players play optimally is denoted by s1(n, #H, F) when Max starts, and by s2(n, #H, F) when Mini starts. We study these values for several natural choices of F and H.<|reference_end|>
@article{patkós2024generalized,
    title={Generalized saturation game},
    author={Bal'azs Patk'os, Milov{s} Stojakovi'c, Jelena Stratijev, M'at'e
  Vizer},
    journal={arXiv preprint arXiv:2404.02288},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.02288},
    primaryClass={math.CO cs.DM}
}