发表机构
University of Illinois, Chicago; University of California, San Diego（伊利诺伊大学芝加哥分校; 加州大学圣迭戈分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明了弧数超过 (t-1)n 的欧拉有向图必含任意 t 边有向树，界紧，是 Erdős-Sós 猜想的有向类比，由 GPT-6 Astra 证明。
AI 中文摘要
本文证明了每个具有 $n$ 个顶点且弧数超过 $(t-1)n$ 的欧拉有向图都包含每条具有 $t$ 条边的有向树。该有向图没有环或重复弧，但允许相反方向的弧。对于每条固定的有向树，该界是紧的，这由完全双向图的并集所证实。此前，即使对于有向路径，这种紧界也是未知的。这可以被视为最近证明的 Erdős-Sós 猜想的有向类比。该结果由 GPT-6 Astra 证明。
英文摘要
It is shown that every Eulerian digraph on $n$ vertices with more than $(t-1)n$ arcs contains every oriented tree with $t$ edges. The digraphs have no loops or repeated arcs, but opposite arcs are permitted. The bound is sharp for each fixed oriented tree, as witnessed by disjoint unions of complete bidirected graphs. Previously, such tight bounds were not known, even just for directed paths. This can be considered as a directed analog of the recently proved Erdős-Sós conjecture. The result was proved by GPT-6 Astra.
Comments10 pages, Eulerian digraph, oriented tree, directed path, extremal graph theory, permutation prefix, Erdős--Sós theorem
