Given a simple graph G with a vertex set V and a set of ‘requirements’ {rvw | v, w ∈ V}, we consider a problem to find a Hamilton cycle minimizing an objective function similar to that in the optimum requirement spanning tree problem studied by Hu. And we show that a particular Hamilton cycle C* which is explicitly definable is a solution to the problem when G is complete and {rvw} satisfies inverse Supnick property closely related to Monge property. It is of great interest that C* is also a solution to the symmetric traveling salesman problem with (not inverse) Supnick property. The result in this paper can be applied to the construction of ring networks with high reliability in case where the inverse Supnick property is naturally assumed.
