Paths with two blocks in oriented graphs of large minimum semi-degree
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866912748638568448 |
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| author | Chen, Bin Hou, Xinmin Zhou, Xinyu |
| author_facet | Chen, Bin Hou, Xinmin Zhou, Xinyu |
| contents | 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 for directed paths by a result from Jackson (JGT, 1981). 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 $P$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04423 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Paths with two blocks in oriented graphs of large minimum semi-degree Chen, Bin Hou, Xinmin Zhou, Xinyu Combinatorics 05C20, 05C38 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 for directed paths by a result from Jackson (JGT, 1981). 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 $P$. |
| title | Paths with two blocks in oriented graphs of large minimum semi-degree |
| topic | Combinatorics 05C20, 05C38 |
| url | https://arxiv.org/abs/2512.04423 |