University of Calgary

# Indivisible homogeneous directed graphs and a game for vertex partitions

## Abstract

Let $\mathcal T$ be a set of finite tournaments. We will give a necessary and sufficient condition for the $\mathcal T$-free homogeneous directed graph $\Ha_{\mathcal T}$ to be {\sl divisible}; that is, that there is a partition of $\Ha_{\mathcal T}$ into two sets neither of which contains an isomorphic copy of $\Ha_{\mathcal T}$.