On the Oriented Diameter of Graphs With Given Minimum Degree

ABSTRACT Erdős et al. proved that the diameter of a connected ‐vertex graph with minimum degree is at most . The oriented diameter of an undirected graph , denoted by , is the minimum diameter of a strongly connected orientation of . Bau and Dankelmann showed that for every bridgeless ‐vertex graph with minimum degree . They also showed an infinite family of graphs with oriented diameter at least and posed the problem of determining the smallest possible value for which holds. In this paper, we asymptotically answer Bau and Dankelmann's question by showing that the smallest value approaches 1 as approaches infinity.