Every large connected Cayley graph with degree at least n to the power 1-c for some fixed c>0 has a Hamilton cycle.
Perfect matchings ino(n 1.5) time in regular bipartite graphs.Combinatorica, 39(2):323–354
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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.