Winkler–Zuckerman blanket-time conjecture for finite graphs

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 $(1-\epsilon)$-approximate blanket time and the cover time of $G$ be defined in the usual way. Winkler–Zuckerman's conjecture. For each $\epsilon\in(0,1)$ there is a constant $K_\epsilon<\infty$ such that

$$\max_{v\in V}\mathbb{E}_v((1-\epsilon)\text{-approximate blanket time of }G)\leq K_\epsilon\cdot\max_{v\in V}\mathbb{E}_v(\text{cover time of }G).$$

This conjecture compares the approximate blanket time with the cover time uniformly over all finite graphs. It was later proved by Ding, Lee and Peres, so the statement is resolved.