A Size Condition for Small Diameter Orientable Graphs
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908500641185792 |
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| author | Boriboon, Sopon Kittipassorn, Teeradej |
| author_facet | Boriboon, Sopon Kittipassorn, Teeradej |
| contents | In 2002, Koh and Tay conjectured that every bridgeless graph of order $n\geq 5$ and size at least ${n\choose 2}-n+5$ has an orientation of diameter two. Later, Cochran, Czabarka, Dankelmann and Székely proved this conjecture and asked what is the minimum number of edges required in a bridgeless graph of order $n$ to guarantee the existence of an orientation of diameter at most $d$? We conjecture that the answer is ${n-d \choose 2}+n+2$. We prove this conjecture for the case $d=n-2$ and prove the lower bound of this conjecture for the case $5\leq d\leq n-2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17569 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Size Condition for Small Diameter Orientable Graphs Boriboon, Sopon Kittipassorn, Teeradej Combinatorics 05C12, 05C20 In 2002, Koh and Tay conjectured that every bridgeless graph of order $n\geq 5$ and size at least ${n\choose 2}-n+5$ has an orientation of diameter two. Later, Cochran, Czabarka, Dankelmann and Székely proved this conjecture and asked what is the minimum number of edges required in a bridgeless graph of order $n$ to guarantee the existence of an orientation of diameter at most $d$? We conjecture that the answer is ${n-d \choose 2}+n+2$. We prove this conjecture for the case $d=n-2$ and prove the lower bound of this conjecture for the case $5\leq d\leq n-2$. |
| title | A Size Condition for Small Diameter Orientable Graphs |
| topic | Combinatorics 05C12, 05C20 |
| url | https://arxiv.org/abs/2508.17569 |