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Hamiltonicity of cubic Cayley graphs

Henry GloverDragan Marušič — 2007

Journal of the European Mathematical Society

Following a problem posed by Lovász in 1969, it is believed that every finite connected vertex-transitive graph has a Hamilton path. This is shown here to be true for cubic Cayley graphs arising from finite groups having a ( 2 , s , 3 ) -presentation, that is, for groups G = a , b a 2 = 1 , b s = 1 , ( a b ) 3 = 1 , generated by an involution a and an element b of order s 3 such that their product a b has order 3 . More precisely, it is shown that the Cayley graph X = Cay ( G , { a , b , b - 1 } ) has a Hamilton cycle when | G | (and thus s ) is congruent to 2 modulo 4, and has a long cycle missing...

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