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Suppose G is a nilpotent, finite group. We show that if {a,b} is any2-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 everyconnected Cayley graph on G that has valence at most 4.

2-generated Cayley digraphs on nilpotent groups have hamiltonian paths