Let G and H be graphs, and G H the strong product of G and H. We prove that for any connected graphs G and H there is a strongly connected orientation D of G H such that diam(D) ≤ 2r + 15, where r is the radius of G H.This improves the general bound diam(D) ≤ 2r 2 +2r for arbitrary graphs, proved by Chvátal and Thomassen.
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