A graph $G$ is perfect if every induced subgraph $H$ of $G$ can be coloured with $k$ colours, where $k$ is the size of a largest clique in $H$.
The Perfect Graph Theorem (conjectured by Berge and proved by Lovasz) states that if $G$ is perfect, then its complement is. My question: to what extent if any is the perfect graph theorem true for infinite graphs?