  Given a weighted graph $G$ with $n$ vertices and $m$ edges, and a positive
integer $p$, the Hamiltonian $p$-median problem consists in finding $p$ cycles
of minimum total weight such that each vertex of $G$ is in exactly one cycle.
We introduce an $O(n^6)$ 3-approximation algorithm for the particular case in
which $p \leq \lceil \frac{n-2\lceil \frac{n}{5} \rceil}{3} \rceil$. An
approximation ratio of 2 might be obtained depending on the number of
components in the optimal 2-factor of $G$. We present computational experiments
comparing the approximation algorithm to an exact algorithm from the
literature. In practice much better ratios are obtained. For large values of
$p$, the exact algorithm is outperformed by our approximation algorithm.
