Class of Hamiltonian-partitionable networks

It is shown that, if the graph G of a network N is the sum of n Hamiltonian circuits, the product G×G of G with itself is the sum of 2n Hamiltonian circuits. For example, C×C, where C is a circuit, is the sum of two Hamiltonian circuits, and K2n+1×K2n+1, where K2n+1 is the complete graph of order 2n+1, is the sum of 2n such circuits.