AI 中文总结
本文在有向图框架下，解决了稠密有向图中生成H-细分图的细分路径长度控制问题，证明了满足度条件的有向图必含路径长度差不超1的生成H-细分图。
AI 中文摘要
Pavez-Signé在《Combin. Probab. Comput.》2024年第33卷第121-128页中提出了关于生成H-细分图的Dirac型条件猜想，并询问细分路径是否可要求长度相近。Lee在《European J. Combin.》2025年第124卷第104059页中在更强的有向图框架下解决了存在性猜想。本文在该有向图框架下回答长度控制问题：对任意ε>0，存在常数C₀>0，使得对每个含h条弧且无孤立顶点的有向图H，每个n顶点有向图D满足n≥C₀h且δ⁰(D)≥(1/2+ε)n时，包含一个生成H-细分图，其细分路径长度相差不超过1。
英文摘要
Pavez-Signé [Combin. Probab. Comput. 33 (2024), 121--128] conjectured a Dirac-type condition for spanning $H$-subdivisions and asked whether the subdivision paths can additionally be required to have similar lengths. Lee [European J. Combin. 124 (2025), 104059] resolved the existence conjecture in the stronger setting of digraphs. We answer the length-control question in this stronger directed setting: for every $\varepsilon>0$, there exists a constant $C_0>0$ such that, for every digraph $H$ with $h$ arcs and no isolated vertices, every $n$-vertex digraph $D$ with $n\ge C_0h$ and $δ^0(D)\ge(1/2+\varepsilon)n$ contains a spanning $H$-subdivision whose subdivision paths have lengths differing by at most one.
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