Lower Bounds on Universal Traversal Sequences for Cycles and Other Low Degree Graphs

Abstract

Universal traversal sequences for cycles require length $\Omega (n^{1.29} )$, improving the previous bound of $\Omega (n\log n)$. For $d \geq 3$, universal traversal sequences for d-regular graphs require length $\Omega (d^{0.71} n^{2.29} )$. For constant d, the best previous bound was $\Omega (n^2 \log n)$.