Hamiltonian decompositions of products of cycles

Abstract

A graph is said to be decomposable into hamiltonian cycles if its edge set can be partitioned into hamiltonian cycles. We show that the cartesian product of any three cycles can be decomposed into three hamiltonian cycles, thus settling a conjecture by Kotzig. We also show that, more generally, the cartesian product of 2 a 3 b graphs, each decomposable into m hamiltonian cycles, can be decomposed into 2 a 3 b m hamiltonian cycles.