Before revision: We prove that , assuming the Strong Exponential Time Hypothesis , for any \delta>0, a 5/3-\delta approximation of the diameter of an undirected unweighted graph with nvertices needs n ^{ 3/2-o(1) time.
After revision: We prove several tight results on the fine-grained complexity of approximating the diameter of a graph. First, we prove that, for any \varepsilon>0 , assuming the Strong Exponential Time Hypothesis , for any \delta>0, a 5/3-\delta approximation of the diameter of an undirected unweighted graph with nvertices needs n ^{ 3/2-o(1) time.