Cover time of random subgraphs of the hypercube

TL;DR

This paper determines the exact cover time for random subgraphs of the hypercube when they are above the connectivity threshold, providing insights into the efficiency of random walks on these graphs.

Contribution

It offers precise calculations of the cover time for $Q_{n,p}$, advancing understanding of random walks on high-dimensional random subgraphs.

Findings

Exact cover time values for $Q_{n,p}$ above connectivity threshold

Insights into random walk efficiency on hypercube subgraphs

Threshold conditions for connectivity and cover time behavior

Abstract

$Q_{n,p}$, the random subgraph of the $n$-vertex hypercube $Q_n$, is obtained by independently retaining each edge of $Q_n$ with probability $p$. We give precise values for the cover time of $Q_{n,p}$ above the connectivity threshold.