论文标题
通过顶点 - 划线盖3-均匀的超图形。
Cover 3-uniform hypergraphs by vertex-disjoint tight paths
论文作者
论文摘要
令$ h $为$ n $ vertex 3均匀的超图，使每对顶点至少在$ n/3+o（n）$边缘中。我们表明，$ h $包含两个顶点 - 局关系的紧密路径，它们的工会涵盖了$ h $的顶点集。这里的数量二是最好的，并且学位条件在渐近上最好。该结果还具有解释为\ emph {缺陷问题}，最近由Nenadov，Sudakov和Wagner提出：每个这样的$ H $都可以通过添加最多两个顶点，并将所有三元组合在一起。
Let $H$ be an $n$-vertex 3-uniform hypergraph such that every pair of vertices is in at least $n/3+o(n)$ edges. We show that $H$ contains two vertex-disjoint tight paths whose union covers the vertex set of $H$. The quantity two here is best possible and the degree condition is asymptotically best possible. This result also has an interpretation as the \emph{deficiency problems}, recently introduced by Nenadov, Sudakov and Wagner: every such $H$ can be made Hamiltonian by adding at most two vertices and all triples intersecting them.
