发表机构
School of Mathematics and Statistics, Fuzhou University; Center for Discrete Mathematics, Fuzhou University（福州大学数学与统计学院; 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。AI 中文总结
本文证明最小半度至少为 3k/8+2 的二分有向图包含所有长度为 k 的两段有向路径，并指出二分情形下阈值与段数密切相关。
AI 中文摘要
Stein 猜想：对于任意整数 $k\geq 2$，每个最小半度大于 $k/2$ 的有向图包含每条长度为 $k$ 的路径的所有定向。最近，Chen、Hou 和 Zhou 证明该猜想对任何具有两段的有向路径成立，其中有向路径的一段是其内部的最大有向子路径。本文证明：每个最小半度至少为 $3k/8+2$ 的二分有向图包含每条长度为 $k$ 的两段有向路径（$k\ge 2$）。此外，与一般有向图情形相反，我们强调二分情形中的最小半度阈值与段数密切相关。
英文摘要
Stein conjectured that for any integer $k\geq 2$, every oriented graph with minimum semidegree greater than $k/2$ contains every orientation of a path with $k$ edges. Recently, Chen, Hou and Zhou proved this conjecture to be true for any oriented path with two blocks, where a block of an oriented path is a maximal directed subpath within it. In this paper, we prove that every bipartite oriented graph with minimum semidegree at least $3k/8+2$ contains every oriented path with two blocks of length $k$ for $k\ge 2$. Moreover, in contrast to the general oriented setting, we highlight that the minimum semidegree threshold in the bipartite setting is closely related to the number of blocks.
