Lower bounds on the length of universal traversal sequences

摘要

Universal traversal sequences for d-regular n-vertex graphs require length Ω(d2n2 + dn2 log(nd)), for 3 ⩽d⩽n3 − 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.