论文标题
树木和树状结构
Trees and tree-like structures in dense digraphs
论文作者
论文摘要
我们证明，具有最大程度的$ n $顶点上的每一个定向的树作为$ n $顶点上的每个有向图的跨度子图显示，最小半透明度至少$ n/2+\ \ \ \ \ \ m atrm {o}（n）$。这可以看作是Komlós，Sárközy和Szemerédi的著名定理的有向图类似物。我们对树的结果取决于更普遍的结果，允许嵌入更宽的跨度“类似树”结构的任意方向，例如最多$ \ mathrm {o}的集合（n^{1/4}）$ tertex-disjoint Cycles and Graphs $ h $ with $ for $ | n）^{ - 1/2}} $，其中每个边缘至少被细分一次。
We prove that every oriented tree on $n$ vertices with bounded maximum degree appears as a spanning subdigraph of every directed graph on $n$ vertices with minimum semidegree at least $n/2+\mathrm{o}(n)$. This can be seen as a directed graph analogue of a well-known theorem of Komlós, Sárközy and Szemerédi. Our result for trees follows from a more general result, allowing the embedding of arbitrary orientations of a much wider class of spanning "tree-like" structures, such as a collection of at most $\mathrm{o}(n^{1/4})$ vertex-disjoint cycles and subdivisions of graphs $H$ with $|H|< n^{(\log n)^{-1/2}}$ in which each edge is subdivided at least once.
