Let G=(V,E) be a directed graph. A set of (directed) edges H (a subset of E) is a Hamiltonian cycle of G, if it is a cycle and goes through each vertex of G exactly once.

INPUT: An directed graph given by the set of ground atoms "vtx(v)", v=1,2,...,n, where n is the number of vertices, and "edge(x,y)" for each directed edge (x,y).

OUTPUT: a set of edges of the graph forming its Hamiltonian cycle (or a message that the graph has no Hamiltonian cycles).

DATA SETS:
In each case, the vertex set is {1,2,...,200}, the edge set has 1250 elements; only the edges are listed in the data sets given below.

hc1  (has Hamiltonian cycles)
hc2  (has Hamiltonian cycles)
hc3  (has Hamiltonian cycles)
hc4  (has Hamiltonian cycles)

hc5  (has no Hamiltonian cycles)
hc6  (has no Hamiltonian cycles)
hc7  (has no Hamiltonian cycles)
hc8  (has no Hamiltonian cycles)
 

NOTES: