English

Some Maker-Breaker games on hypergraphs

Combinatorics 2025-09-04 v1

Abstract

We consider some biased Maker-Breaker games. Starting with the complete kk-uniform hypergraph on nn vertices, at each turn Maker claims one edge, and then Breaker claims bb 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 mm, or having a full-rank incidence matrix, or having a Berge Hamilton cycle or having a perfect matching or a Hamilton \ell-cycle.

Keywords

Cite

@article{arxiv.2509.02788,
  title  = {Some Maker-Breaker games on hypergraphs},
  author = {Patrick Bennett and Alan Frieze and Wesley Pegden},
  journal= {arXiv preprint arXiv:2509.02788},
  year   = {2025}
}
R2 v1 2026-07-01T05:18:15.162Z