有向图的交集
Intersections of Directed Graphs
- Center for Discrete Mathematics, Fuzhou University（福州大学离散数学中心）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文研究加权有向图在重标记下的重叠偏差及随机放置时交集分布的集中性，得到与加权超图情形类似的结果。
中文摘要 AI 辅助
给定两个阶为\(n\)的加权有向图，我们研究在重新标记下，它们的重叠程度与其随机平均值相比可能偏离多少，以及当它们随机放置时，其交集分布的集中程度。Bollobás和Scott在加权\(k\)-一致超图上研究了这些问题，并提出了有向图的相应问题。在本文中，我们研究了加权有向图的这些问题，并获得了与加权超图情形类似的结果。
英文摘要
Given two weighted directed graphs of order \(n\), we study how much their overlap can deviate from its random average under relabelling, and how concentrated the distribution of their intersection is when they are placed at random. Bollobás and Scott studied these problems on weighted $k$-uniform hypergraphs and raised the corresponding questions for directed graphs. In this paper, we study these problems for weighted directed graphs and obtain results analogous to those in the weighted hypergraph setting.
