An improved upper bound on the oriented diameter of graphs with diameter $4$
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911673298714624 |
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| author | Lin, Jifu You, Lihua |
| author_facet | Lin, Jifu You, Lihua |
| contents | Let $f(d)$ be the smallest value for which every bridgeless graph $G$ with diameter $d$ admits a strong orientation $\overrightarrow{G}$ such that the diameter of $\overrightarrow{G}$ is at most $f(d)$. Chvátal and Thomassen (1978) established general bounds for $f(d)$ which implies $f(4)\geq 12$, and proved $f(2)=6$. Kwok et al. (2010) proved that $9\leq f(3)\leq 11$. Wang and Chen (2022) determined $f(3)=9$. Babu et al. (2021) showed $f(4)\leq 21$. In this paper, we improve the upper bound of $ f(4) $ to $18$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_11667 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An improved upper bound on the oriented diameter of graphs with diameter $4$ Lin, Jifu You, Lihua Combinatorics 05C12, 05C20 Let $f(d)$ be the smallest value for which every bridgeless graph $G$ with diameter $d$ admits a strong orientation $\overrightarrow{G}$ such that the diameter of $\overrightarrow{G}$ is at most $f(d)$. Chvátal and Thomassen (1978) established general bounds for $f(d)$ which implies $f(4)\geq 12$, and proved $f(2)=6$. Kwok et al. (2010) proved that $9\leq f(3)\leq 11$. Wang and Chen (2022) determined $f(3)=9$. Babu et al. (2021) showed $f(4)\leq 21$. In this paper, we improve the upper bound of $ f(4) $ to $18$. |
| title | An improved upper bound on the oriented diameter of graphs with diameter $4$ |
| topic | Combinatorics 05C12, 05C20 |
| url | https://arxiv.org/abs/2605.11667 |