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arXiv · 2509.02788

Some Maker-Breaker games on hypergraphs

Patrick Bennett·Alan Frieze·Wesley Pegden
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Abstract

We consider some biased Maker-Breaker games. Starting with the complete $k$-uniform hypergraph on $n$ vertices, at each turn Maker claims one edge, and then Breaker claims $b$ edges. Maker's goal is to obtain a set of edges having some increasing property. We consider the case where Maker's desired property is minimum degree $m$, or having a full-rank incidence matrix, or having a Berge Hamilton cycle or having a perfect matching or a Hamilton $\ell$-cycle.

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Patrick Bennett, Alan Frieze, Wesley Pegden. 2025-09-02. Some Maker-Breaker games on hypergraphs. https://arxiv.org/abs/2509.02788

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