Hamiltonian cycles decomposition of two cycles’s composite

Abstract

A.Kǒtzig had studied Hamilton decomposition, he had proved that cartesian product of two cycles decomposable into hamiltonian cycles. Bermond J.C. came up with some conjectures in [1], the conjectures 1.15 that C_m[C_n] can be decomposed into n + 1 edge-disjoint Hamilton circuits . In this paper, we had proved that the conjecture.

Keywords:

• Hamilton decomposition
• Composite
• Cycle

2000 Mathematics Subject Classifications:

• 05C35
• 05C75
• 05C60