The cover time of a biased random walk on a random cubic graph

TL;DR

This paper analyzes the cover times of a biased random walk on random cubic graphs, providing asymptotically accurate estimates for how long it takes to visit all vertices and edges.

Contribution

It introduces a biased random walk model and derives precise asymptotic estimates for vertex and edge cover times on random cubic graphs.

Findings

Vertex cover time is approximately n log n.

Edge cover time is approximately 1.5 n log n.

Provides asymptotically correct estimates for cover times.

Abstract

We study a random walk that prefers tou se unvisited edges in the context of random cubic graphs. We establish asymptotically correct estimates for the vertex and edge cover times, these being $\approx n\log n$ and $\approx \frac32n\log n$ respectively.