Separating Path Systems in Complete Graphs

We prove that in any n-vertex complete graph there is a collection 𝒫 of (1 + o(1))n paths that strongly separates any pair of distinct edges e, f, meaning that there is a path in 𝒫 which contains e but not f. Furthermore, for certain classes of n-vertex α n -regular graphs we find a collection of (√(3 α + 1) - 1 + o(1))n paths that strongly separates any pair of edges. Both results are best-possible up to the o(1) term.