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arXiv · 2508.17569

A Size Condition for Small Diameter Orientable Graphs

Sopon Boriboon·Teeradej Kittipassorn
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Abstract

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 $5\leq d\leq n-2$.

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Sopon Boriboon, Teeradej Kittipassorn. 2025-08-25. A Size Condition for Small Diameter Orientable Graphs. https://arxiv.org/abs/2508.17569

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