AI 中文总结
本文针对现有两种有向平墙定理的缺陷，提出一种排除交叉行网格的新有向平墙定理，其证明基于已有成果并适配自身设定，填补了相关定理的中间空白。
AI 中文摘要
图子式项目包含了近期无向图论研究中最具影响力的成果。近年来，在将部分成果推广至有向图方面已取得进展，包括Kawarabayashi与Kreutzer的有向网格定理[STOC '15]，以及Giannopoulou、Kawarabayashi、Kreutzer与Kwon的有向平墙定理[SODA '22]。本文讨论现有两种版本的有向平墙定理及其缺陷，随后提出一种替代的有向平墙定理，该定理将另一种有向图排除为蝴蝶子式。此新定理介于两种现有定理之间，因此不具备上述两种缺陷。本文平墙定理的证明基于Giannopoulou等人[SODA '22]的证明，该证明已由Giannopoulou与Wiederrecht[STOC '24]调整，本文为适配自身设定进一步作出调整。
英文摘要
The graph minor project contains the most influential results in recent undirected graph theory research. There has been progress in recent years in generalising some of their results to directed graphs, with the directed grid theorem of Kawarabayashi and Kreutzer [STOC '15] and the directed flat wall theorem of Giannopoulou, Kawarabayashi, Kreutzer, and Kwon [SODA '22]. We discuss the two different versions of the existing directed flat wall theorem and their drawbacks. Then, we present an alternative directed flat wall theorem that excludes a different digraph as a butterfly minor. This new theorem lies ``in between'' the two existing ones and, as such, does not have either of these drawbacks. The proof of our flat wall theorem is based on the one by Giannopoulou, Kawarabayashi, Kreutzer, and Kwon [SODA '22], which has been adapted by Giannopoulou and Wiederrecht [STOC~'24]. Here we make further adjustments to match our setting.
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