Hamiltonian decompositions of Cayley graphs on abelian groups of even order

Abstract

Alspach conjectured that any 2 k-regular connected Cayley graph cay( A, S) on a finite abelian group A can be decomposed into k hamiltonian cycles. In 1992, the author proved that the conjecture holds if S={s 1,s 2, …, s k} is a minimal generating set of an abelian group A of odd order. Here we prove an analogous result for abelian group of even order: If A is a finite abelian group of even order at least 4 and S={s 1,s 2, …, s k} is a strongly minimal generating set (i.e., 2 s i ∉〈 S−{ s i }〉 for each 1⩽ i⩽ k) of A, then cay( A, S) can be decomposed into hamiltonian cycles.