  Let $G^n$ be a graph on $n$ vertices and let $w_k(G^n)$ denote the number of
walks of length $k$ in $G^n$ divided by $n$. Erd\H{o}s and Simonovits
conjectured that $w_k(G^n)^t \geq w_t(G^n)^k$ when $k\geq t$ and both $t$ and
$k$ are odd. We prove this conjecture.
