  In this short note we prove a lower bound for the MaxCut of a graph in terms
of the Lov\'asz theta function of its complement. We combine this with known
bounds on the Lov\'asz theta function of complements of $H$-free graphs to
recover many known results on the MaxCut of $H$-free graphs. In particular, we
give a new, very short proof of a conjecture of Alon, Krivelevich and Sudakov
about the MaxCut of graphs with no cycles of length $r$.
