2-generated Cayley digraphs on nilpotent groups have hamiltonian paths

Abstract

Suppose G is a nilpotent, finite group. We show that if {a,b} is any 2-element generating set of G, then the corresponding Cayley digraph Cay(G;a,b) has a hamiltonian path. This implies there is a hamiltonian path in every connected Cayley graph on G that has valence at most 4.

7 pages, no figures; corrected a few typographical errors