6 problems

Let $G$ be a finite graph with vertex set $V$. For a starting vertex $v\in V$, write $\mathbb{E}_v$ for expectation for the simple random walk started at $v$, and let the…

Let $G$ be a rooted graph on $n$ vertices, with root $r$, and let $cc_r(G)$ and $CT_r(G)$ denote its cover cost and cover time from $r$. The path on $n$ vertices rooted at an endpo…

Let $G_w$ be a graph equipped with the minimum-degree weighting scheme, let $n$ be its number of vertices, and let $d$ be the parameter used in the locally tree-like analysis. Let…

Let $G=(V,E)$) be a graph. For a random walk on $G$, let $\text{{\bf COV}}[G]$ denote its cover time and let $\text{{\bf BCOV}}[G]$ denote the blanket-cover time, the expected firs…

Let $G$ be a graph on $n$ vertices, let $k$ satisfy $n\geq k\geq 1$, and write $S^k(G)$ for the speed-up in covering the graph. Logarithmic speed-up conjecture. For any graph $G$ a…

Let $G$ be a graph, let $k\geq 1$ be the number of random walks, and write $S^k(G)$ for their speed-up in covering the graph. Linear speed-up conjecture. For any graph $G$ and any…