Every large connected Cayley graph with degree at least n to the power 1-c for some fixed c>0 has a Hamilton cycle.
Hamiltonian degree sequences in digraphs.Journal of Combinatorial Theory, Series B, 100(4):367–380
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The Lov\'asz conjecture holds for moderately dense Cayley graphs
Every large connected Cayley graph with degree at least n to the power 1-c for some fixed c>0 has a Hamilton cycle.