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An improved upper bound for oriented diameter of graphs with diameter $4$
Let $f(d)$ denote the smallest integer such that every bridgeless graph of diameter $d$ admits a strong orientation with diameter at most $f(d)$. It is known that $f(2)=6$ and $f(3)=9$. For $d=4$, the classical bounds of Chvátal and Thomassen [JCTB, 1978] imply $12\le f(4)\le40$, and subsequent work
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