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Bounds for the minimum oriented diameter

Abstract : We consider the problem of determining an orientation with minimum diameter MOD(G) of a connected and bridge-less graph G. In 2001 Fomin et al. discovered the relation MOD(G) <= 9 gamma(G) - 5 between the minimum oriented diameter and the size gamma(G) of a minimum dominating set. We improve their upper bound to MOD(G) <= 4 gamma(G).
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Sascha Kurz, Martin Laetsch. Bounds for the minimum oriented diameter. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2012, Vol. 14 no. 1 (1), pp.109-140. ⟨hal-00990564⟩

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