发表机构
Fudan University; Westlake University; ShanghaiTech University（复旦大学; 西湖大学; 上海科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明了六顶点上自补完备化的阈值 \\(\cthreshold(6)=7\\)，并确定了八弧障碍层的五个同构类，表明普通打包弱于同阶自补完备化。
AI 中文摘要
设 \\(\cthreshold(n)\\) 为最大的整数 \\(q\\)，使得每个具有至多 \\(q\\) 条弧的 \\(n\\) 个顶点上的无环有向图都同构于某个 \\(n\\) 阶自补有向图的生成子有向图。我们证明 \\(\cthreshold(6)=7\\)。上界由 \\(\bK{3}\dunion (x\longrightarrow y\longrightarrow z)\\) 给出，并通过自补置换的直接论证得出。我们还确定了完整的八弧障碍层：它由五个同构类组成，或在识别互逆有向图后为三个。所有五个都是弧极小的。然而，每个都能与自身的同构副本打包，因此在这个首次失败层中，普通打包严格弱于同阶自补完备化。
英文摘要
Let \(\cthreshold(n)\) be the largest integer \(q\) such that every loopless digraph on \(n\) vertices with at most \(q\) arcs is isomorphic to a spanning subdigraph of a self-complementary digraph of order \(n\). We prove that \(\cthreshold(6)=7\). The upper bound is witnessed by \[ \bK{3}\dunion (x\longrightarrow y\longrightarrow z), \] and follows from a direct argument with a self-complementing permutation. We also determine the complete eight-arc obstruction layer: it consists of five isomorphism classes, or three after converse digraphs are identified. All five are arc-minimal. Each nevertheless packs with an isomorphic copy of itself, so ordinary packing is strictly weaker than same-order self-complementary completion already at this first failure layer.
