In 1978, Chvátal and Thomassen proved that every 2-edge-connected graph with diameter 2 has an orientation with diameter at most 6. They also gave general bounds on the smallest value f (d) such that every 2-edge-connected graph G with diameter d has an orientation with diameter at most f (d). For d = 3, their general bounds reduce to 8 ≤ f (3) ≤ 24. We improve these bounds to 9 ≤ f (3) ≤ 11. © 2009 Elsevier Inc. All rights reserved.
Kwok, P. K., Liu, Q., & West, D. B. (2010). Oriented diameter of graphs with diameter 3. Journal of Combinatorial Theory. Series B, 100(3), 265–274. https://doi.org/10.1016/j.jctb.2009.08.003