Geodesic
Paths with two blocks in oriented graphs of large minimum semi-degree
Bin Chen ; Xinmin Hou1 ; Xinyu Zhou
1University of Science and Technology of China
The electronic journal of combinatorics, Tome 32 (2025) no. 4
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Stein (2020) conjectured that for any positive integer $k$, every oriented graph of minimum semi-degree greater than $k/2$ contains every oriented path of length $k$. This conjecture is true by a result from Jackson (JGT, 1981), where he demonstrated that every oriented graph of minimum semi-degree at least $k/2$ includes a directed path of length $k$. In this paper, we establish the validity of Stein's conjecture specifically for any oriented path with two blocks, where, a block of an oriented path $P$ refers to a maximal directed subpath within $P$.
DOI : 10.37236/13005
Classification : 05C20, 05C38

Bin Chen    ; Xinmin Hou  1   ; Xinyu Zhou 

1 University of Science and Technology of China 
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     author = {Bin Chen and Xinmin Hou and Xinyu Zhou},
     title = {Paths with two blocks in oriented graphs of large minimum semi-degree},
     journal = {The electronic journal of combinatorics},
     year = {2025},
     volume = {32},
     number = {4},
     doi = {10.37236/13005},
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Bin Chen; Xinmin Hou; Xinyu Zhou. Paths with two blocks in oriented graphs of large minimum semi-degree. The electronic journal of combinatorics, Tome 32 (2025) no. 4. doi: 10.37236/13005

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