Avoider-Enforcer games played on edge disjoint hypergraphs

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.