Yin and Wu's size interpolation conjecture for 2-connected subgraphs

Let $G$ be a 2-connected graph of order $n$ and size $m$.

Yin and Wu's size interpolation conjecture. If

$$m \geqslant \frac{1}{2}n^{\frac{3}{2}},$$

then $G$ has a $2$-connected subgraph of order $k$ for each $k\in\{4,\ldots,n\}$.

The conjecture is explicitly stated by Yin and Wu and is disproved in the present paper by construction of counterexamples.