Let G be a connected bridgeless graph with domination number γ. The oriented diameter (strong diameter) of G is the smallest integer d for which G admits a strong orientation with diameter (strong diameter) d. Kurz and Lätsch (2012) conjectured the oriented diameter of G is at most 7γ+12 and the bound is sharp. In this paper, we confirm the conjecture by induction on γ through contracting an unavoidable alternative subgraph, which holds potential for future applications. Moreover, we show the oriented strong diameter of G is at most 7γ-1 by using the same recursive structure, and the bound is best possible.
Wang et al. (Thu,) studied this question.