The Avoider-Enforcer game on hypergraphs of rank 3
Combinatorics
2025-03-28 v1 Discrete Mathematics
Abstract
In the Avoider-Enforcer convention of positional games, two players, Avoider and Enforcer, take turns selecting vertices from a hypergraph H. Enforcer wins if, by the time all vertices of H have been selected, Avoider has completely filled an edge of H with her vertices; otherwise, Avoider wins. In this paper, we first give some general results, in particular regarding the outcome of the game and disjoint unions of hypergraphs. We then determine which player has a winning strategy for all hypergraphs of rank 2, and for linear hypergraphs of rank 3 when Avoider plays the last move. The structural characterisations we obtain yield polynomial-time algorithms.
Cite
@article{arxiv.2503.21672,
title = {The Avoider-Enforcer game on hypergraphs of rank 3},
author = {Florian Galliot and Valentin Gledel and Aline Parreau},
journal= {arXiv preprint arXiv:2503.21672},
year = {2025}
}