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. This result improves on lower bounds of Backurs, Roditty, Segal, Vassilevska-Williams, and Wein ) for the Diameter of a sparse directed unweighted graph can be ruled out by a deterministic SETH-based reduction for every \delta\in(0,1) and essentially every \varepsilon\in(0,1), assuming NSETH.
After 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) 1.499 ) for the Diameter of a sparse directed unweighted graph can be ruled out by a deterministic SETH-based reduction for every \delta\in(0,1) and essentially every \varepsilon\in(0,1), assuming NSETH.