  In 1975 Pippenger and Golumbic proved that any graph on $n$ vertices admits
at most $2e(n/k)^k$ induced $k$-cycles. This bound is larger by a
multiplicative factor of $2e$ than the simple lower bound obtained by a blow-up
construction. Pippenger and Golumbic conjectured that the latter lower bound is
essentially tight. In the present paper we establish a better upper bound of
$(128e/81) \cdot (n/k)^k$. This constitutes the first progress towards proving
the aforementioned conjecture since it was posed.
