Avoider-Enforcer games played on edge disjoint hypergraphs

TL;DR

This paper studies Avoider-Enforcer games on edge disjoint hypergraphs, offering new winning conditions for both players and applying these results to various related game scenarios.

Contribution

It introduces a framework for analyzing Avoider-Enforcer games on hypergraphs, extending classic game results to new settings and providing sufficient conditions for player wins.

Findings

Provided a sufficient condition for Avoider to win.

Provided a sufficient condition for Enforcer to win.

Applied results to multiple Avoider-Enforcer game variants.

Abstract

We analyze Avoider-Enforcer games played on edge disjoint hypergraphs, providing an analog of the classic and well known game $Box$, due to Chv\'{a}tal and Erd\H{o}s. We consider both strict and monotone versions of Avoider-Enforcer games, and for each version we give a sufficient condition to win for each player. We also present applications of our results to several general Avoider-Enforcer games.