  Let $G$ be a graph of even order, and consider $K_G$ as the complete graph on
the same vertex set as $G$. A perfect matching of $K_G$ is called a pairing of
$G$. If for every pairing $M$ of $G$ it is possible to find a perfect matching
$N$ of $G$ such that $M \cup N$ is a Hamiltonian cycle of $K_G$, then $G$ is
said to have the Pairing-Hamiltonian property, or PH-property, for short. In
2007, Fink [J. Combin. Theory Ser. B, 97] proved that for every $d\geq 2$, the
$d$-dimensional hypercube $\mathcal{Q}_d$ has the PH-property, thus proving a
conjecture posed by Kreweras in 1996. In this paper we extend Fink's result by
proving that given a graph $G$ having the PH-property, the prism graph
$\mathcal{P}(G)$ of $G$ has the PH-property as well. Moreover, if $G$ is a
connected graph, we show that there exists a positive integer $k_0$ such that
the $k^{\textrm{th}}$-prism of a graph $\mathcal{P}^k(G)$ has the PH-property
for all $k \ge k_0$.
