Oriented diameter of graphs with given domination number
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912497764663296 |
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| author | Wang, Xiaolin Chen, Yaojun |
| author_facet | Wang, Xiaolin Chen, Yaojun |
| contents | Let $G$ be a connected bridgeless graph with domination number $γ$. The oriented diameter (strong diameter) of $G$ is the smallest integer $d$ for which $G$ admits a strong orientation with diameter (strong diameter) $d$. Kurz and Lätsch (2012) conjectured the oriented diameter of $G$ is at most $\lceil \frac{7γ+1}{2}\rceil$ and the bound is sharp. In this paper, we confirm the conjecture by induction on $γ$ through contracting an unavoidable alternative subgraph, which holds potential for future applications. Moreover, we show the oriented strong diameter of $G$ is at most $7γ-1$ by using the same recursive structure, and the bound is best possible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15997 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Oriented diameter of graphs with given domination number Wang, Xiaolin Chen, Yaojun Combinatorics Let $G$ be a connected bridgeless graph with domination number $γ$. The oriented diameter (strong diameter) of $G$ is the smallest integer $d$ for which $G$ admits a strong orientation with diameter (strong diameter) $d$. Kurz and Lätsch (2012) conjectured the oriented diameter of $G$ is at most $\lceil \frac{7γ+1}{2}\rceil$ and the bound is sharp. In this paper, we confirm the conjecture by induction on $γ$ through contracting an unavoidable alternative subgraph, which holds potential for future applications. Moreover, we show the oriented strong diameter of $G$ is at most $7γ-1$ by using the same recursive structure, and the bound is best possible. |
| title | Oriented diameter of graphs with given domination number |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2506.15997 |