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arXiv · 2404.02288

Generalized saturation game

Balázs Patkós·Miloš Stojaković·Jelena Stratijev·Máté Vizer
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Abstract

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.

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Balázs Patkós, Miloš Stojaković, Jelena Stratijev, Máté Vizer. 2024-04-02. Generalized saturation game. https://doi.org/10.1016/j.dam.2025.05.014

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