Tight Codegree Condition for the Existence of Loose Hamilton Cycles in 3-Graphs

摘要

In 2006, K"{u}hn and Osthus showed that if a 3-graph H on n vertices hasminimum co-degree at least (1/4 +o(1))n and n is even then H has a looseHamilton cycle. In this paper, we prove that the minimum co-degree of n/4suffices. The result is tight.