Liu and Ning's interpolation conjecture for 2-connected subgraphs

For a fixed integer $q\ge 3$, let $n_0(q)$ be an integer threshold. Let $G$ be a 2-connected graph of order $n\ge n_0(q)$, and write $\delta(G)$ for its minimum degree. Liu and Ning's conjecture. Every such graph satisfying

$$\delta(G)\ge \frac{n}{q}$$

contains a $2$-connected subgraph of order $\ell$ for every $\ell\in\{4,5,\ldots,n\}$. This conjecture seeks an asymptotic minimum-degree threshold guaranteeing 2-connected subgraphs of every possible order; the preceding results establish stronger degree thresholds, namely approximately $n/3$ and $n/4$, but the proposed $n/q$ threshold for every fixed $q\ge 3$ remains unresolved.