Ruskey and Savage in 1993 asked whether every matching in a hypercube can be extended to a

Hamiltonian cycle.

Applying Lemma 6, we conclude that H has a

Hamiltonian cycle C, and we obtain the desired result that V(D) = V([C.

Speaking of a

Hamiltonian cycle system of order [upsilon], or HCS([upsilon]) for short, we mean a set of

Hamiltonian cycles of [K.

The midpoints of the edges of a

hamiltonian cycle in the 1-skeleton of a regular tetrahedron T are the vertices of a square.

The

hamiltonian cycle for the cases m = 10 and m = 11 are shown in the Figures 2.

If the degree sum of any two nonadjacent vertices is at least n, then G has a

Hamiltonian Cycle.

In this paper we prove that a through-vertex

Hamiltonian cycle exists in any triangular or tetrahedral grid under very mild conditions, and that there exist quadrilateral and hexahedral grids for which no unconstrained Hamiltonian path exists.

This special type of path is called a

Hamiltonian cycle.

A

Hamiltonian cycle of G is a cycle that traverses every vertex of G exactly once.

A trivial lower bound of 2 (for n [greater than or equal to] 4) is obtained from a minimum weight

Hamiltonian cycle in K(P), because this cycle is plane and consists of two edge-disjoint matchings.

To determine the Hamiltonian circuit it self is a NP-complete problem and when shortest distance and minimum time is added with the

Hamiltonian Cycle, it becomes a very hard optimization problem in the field of operations research.

In fact, the edges of the polygon define a

Hamiltonian cycle in G.