Every large connected Cayley graph with degree at least n to the power 1-c for some fixed c>0 has a Hamilton cycle.
A Szemer´ edi-type regularity lemma in abelian groups, with applications.Geometric & Func- tional Analysis GAF A, 15(2):340–376
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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.