  The generalised Sudoku problem with $N$ symbols is known to be NP-complete,
and hence is equivalent to any other NP-complete problem, even for the standard
restricted version where $N$ is a perfect square. In particular, generalised
Sudoku is equivalent to the, classical, Hamiltonian cycle problem. A
constructive algorithm is given that reduces generalised Sudoku to the
Hamiltonian cycle problem, where the resultant instance of Hamiltonian cycle
problem is sparse, and has $O(N^3)$ vertices. The Hamiltonian cycle problem
instance so constructed is a directed graph, and so a (known) conversion to
undirected Hamiltonian cycle problem is also provided so that it can be
submitted to the best heuristics. A simple algorithm for obtaining the valid
Sudoku solution from the Hamiltonian cycle is provided. Techniques to reduce
the size of the resultant graph are also discussed.
