Exact induced-degenerate-subgraph ratio conjecture for k-degenerate graphs

Let $\alpha_d(k)$ denote the infimum, over $k$-degenerate graphs, of the ratio of the order of a largest induced $d$-degenerate subgraph to the number of vertices. Induced-degenerate-subgraph ratio conjecture for $k\geq 3$. For all integers $k\geq 3$ and $d$ with $k>d$,

$$\alpha_d(k)=\frac{d+1}{k+1}.$$

This assertion is motivated by computational experiments and would determine the exact ratios for the indicated parameters. The source presents it as open.