  A Hamiltonian graph $G$ of order $n$ is $k$-ordered, $2\leq k \leq n$, if for
every sequence $v_1, v_2, \ldots ,v_k$ of $k$ distinct vertices of $G$, there
exists a Hamiltonian cycle that encounters $v_1, v_2, \ldots , v_k$ in this
order. In this paper, answering a question of Ng and Schultz, we give a sharp
bound for the minimum degree guaranteeing that a graph is a $k$-ordered
Hamiltonian graph under some mild restrictions. More precisely, we show that
there are $\varepsilon, n_0> 0$ such that if $G$ is a graph of order $n\geq
n_0$ with minimum degree at least $\lceil \frac{n}{2} \rceil + \lfloor
\frac{k}{2} \rfloor - 1$ and $2\leq k \leq \eps n$, then $G$ is a $k$-ordered
Hamiltonian graph. It is also shown that this bound is sharp for every $2\leq k
\leq \lfloor \frac{n}{2} \rfloor$.
