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The Avoider-Enforcer Game in Hypergraphs of Rank 3

Year: 2026

Type: article

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.

Source: The Electronic Journal of Combinatorics

DOI: 10.37236/14014

Authors: Florian Galliot, Valentin Gledel, Aline Parreau

Institutions: Institut de Mathématiques de Marseille, Le LAMA, Université Savoie Mont Blanc

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4415059689

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