Asymptotic minimum-degree interpolation conjecture for 2-connected subgraphs

Let $G$ be a 2-connected graph of order $n$, and let $\delta(G)$ denote its minimum degree.

Asymptotic interpolation conjecture. If $k\geqslant3$ and

$$\delta(G)\geqslant\frac{n}{k},$$

then there exists an integer $n_0=f(k)$ such that, whenever $n\geqslant n_0$, $G$ has a $2$-connected subgraph of order $\ell$ for each $\ell\in\{4,\ldots,n\}$.

This is proposed as a weaker alternative to Yin and Wu's minimum-degree conjecture. The paper motivates it by noting that the authors suspect the stronger conjecture is false for infinitely many values of $n$; whether this asymptotic statement holds remains open in the supplied text.