On Cayley Digraphs That Do Not Have Hamiltonian Paths. (26th December 2013) - Morris, Dave Witte
Abstract : We construct an infinite family{ C a y → ( G i ; a i ; b i ) } of connected, 2 -generated Cayley digraphs that do not have hamiltonian paths, such that the orders of the generatorsa i andb i are unbounded. We also prove that ifG is any finite group with| [ G, G ] | ≤ 3, then every connected Cayley digraph onG has a hamiltonian path (but the conclusion does not always hold when| [ G, G ] | = 4 or5 ).