2-generated Cayley digraphs on nilpotent groups have hamiltonian paths
classification
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keywords
cayleyhamiltoniannilpotentpathconnectedcorrespondingdigraphdigraphs
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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.
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