Lower bounds on the length of universal traversal sequences

Universal traversal sequences for d-regular n-vertex graphs require length Ω(d2n2 + dn2 log( n d)), for 3 ≤d≤ n 3 - 2. This is nearly tight for d = Θ(n). We also introduce and study several variations on the problem, e.g., edge-universal traversal sequences, showing how improved lower bounds on these would improve the bounds given above. © 1992.