Oriented diameter of the complete tripartite graph (III)
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912239842230272 |
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| author | Liu, Jing Rao, Guang Zhou, Hui |
| author_facet | Liu, Jing Rao, Guang Zhou, Hui |
| contents | Given a bridgeless graph $G$, let $\mathbb{D}(G)$ be the set of all strong orientations of $G$, and define the oriented diameter $f(G)$ of $G$ to be the minimum of diameters $diam(D)$ among all the strong orientations $D\in \mathbb{D}(G)$, i.e., $f(G)=\min\{diam(D)\mid D\in \mathbb{D}(G)\}$. In this paper, we determine the oriented diameter of complete tripartite graph $K(3,p,q)$ for $p\geqslant 5$. Combining with the previous results, the oriented diameter of complete tripartite graph $K(3,p,q)$ are known. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_14903 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Oriented diameter of the complete tripartite graph (III) Liu, Jing Rao, Guang Zhou, Hui Combinatorics 05C20, 05C12 Given a bridgeless graph $G$, let $\mathbb{D}(G)$ be the set of all strong orientations of $G$, and define the oriented diameter $f(G)$ of $G$ to be the minimum of diameters $diam(D)$ among all the strong orientations $D\in \mathbb{D}(G)$, i.e., $f(G)=\min\{diam(D)\mid D\in \mathbb{D}(G)\}$. In this paper, we determine the oriented diameter of complete tripartite graph $K(3,p,q)$ for $p\geqslant 5$. Combining with the previous results, the oriented diameter of complete tripartite graph $K(3,p,q)$ are known. |
| title | Oriented diameter of the complete tripartite graph (III) |
| topic | Combinatorics 05C20, 05C12 |
| url | https://arxiv.org/abs/2502.14903 |