Work

Oriented paths with two blocks in bipartite oriented graphs

Year: 2026

Type: preprint

Abstract: 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.09935

Authors: Chen, Bin, Chen, Meishuang, Hou, Xinmin, Zhou, Xinyu

Institutions: Fuzhou University, Center for Discrete Mathematics and Theoretical Computer Science, University of Science and Technology of China, Hefei University of Technology, Southwest Petroleum University

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, National Science and Technology Major Project

Awards: G3102504474, G3685485237, G3857364911, G6342197334

OpenAlex ID: W7212189575

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