Avoider-Enforcer games played on edge disjoint hypergraphs

Abstract

We analyze Avoider-Enforcer games played on edge disjoint hypergraphs, providing an analog of the classic and well known game $Box$, due to Chvátal and Erdős. 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.