  We study the computational complexity of Feedback Vertex Set on subclasses of
Hamiltonian graphs. In particular, we consider Hamiltonian graphs that are
regular or are planar and regular. Moreover, we study the less known class of
$p$-Hamiltonian-ordered graphs, which are graphs that admit for any $p$-tuple
of vertices a Hamiltonian cycle visiting them in the order given by the tuple.
We prove that Feedback Vertex Set remains NP-hard in these restricted cases,
even if a Hamiltonian cycle is additionally given as part of the input.
