论文标题
汉密尔顿$（k/2）$ - $ k $均匀超图的最低学位阈值
Minimum degree thresholds for Hamilton $(k/2)$-cycles in $k$-uniform hypergraphs
论文作者
论文摘要
For any even integer $k\ge 6$, integer $d$ such that $k/2\le d\le k-1$, and sufficiently large $n\in (k/2)\mathbb N$, we find a tight minimum $d$-degree condition that guarantees the existence of a Hamilton $(k/2)$-cycle in every $k$-uniform hypergraph on $n$ vertices.当$ n \ in K \ Mathbb n $中时，该学位条件与Rödl，Ruciński和Szemerédi提供的完美匹配的存在相吻合（以$ d = k-1 $）和Treglown和Zhao（$ d = k-1 $）和Zhao（$ d \ ge k/2 $），因此我们的结果会在这种情况下得到增强。
For any even integer $k\ge 6$, integer $d$ such that $k/2\le d\le k-1$, and sufficiently large $n\in (k/2)\mathbb N$, we find a tight minimum $d$-degree condition that guarantees the existence of a Hamilton $(k/2)$-cycle in every $k$-uniform hypergraph on $n$ vertices. When $n\in k\mathbb N$, the degree condition coincides with the one for the existence of perfect matchings provided by Rödl, Ruciński and Szemerédi (for $d=k-1$) and Treglown and Zhao (for $d\ge k/2$), and thus our result strengthens theirs in this case.
