Hamiltonian paths in Cayley digraphs of finitely-generated infinite abelian groups

AbstractWe show every finitely-generated, infinite abelian group (i.e. Zn x G where G is a finite abelian group) has a minimal generating set for which the Cayley digraph has a two-way infinite hamiltonian path, and if n⩾2, then this Cayley digraph also has a one-way infinite hamiltonian path. We show further that in the case of Zn (n⩾2), the Cayley digraph is 2-ply hamiltonian