2 problems

A hypergraph is a pair consisting of a vertex set and a collection of subsets of that vertex set, called hyperedges. In the Tic-Tac-Toe game on a hypergraph, Maker wins if Maker ca…

Let $d,m,n$ be positive integers, and consider the Maker–Breaker game on $\mathbb Z^d$ in which the winning sets consist of $m$ consecutive gridpoints in one of $n$ given direction…