Lower bounds on the length of universal traversal sequences

Abstract

Universal traversal sequences for d-regular n-vertex graphs require length Ω(d 2n 2 + dn 2 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.