Zhang–Zhang conjecture on equitable degenerate colouring

Let $\Delta,d,k\in\mathbb{Z}$, with $d\geq 0$. A graph is $d$-degenerate if every subgraph contains a vertex of degree at most $d$; an equitable $d$-degenerate $k$-colouring is a $k$-colouring whose colour classes induce $d$-degenerate graphs and whose class sizes differ pairwise by at most one.

Zhang–Zhang conjecture. If

$$k\geq \frac{\Delta+1}{d+1},$$

then every graph with maximum degree at most $\Delta$ has an equitable $d$-degenerate $k$-colouring.

The supplied source gives no resolution of this conjecture. It presents it as the degenerate-colouring analogue of the equitable tree-colouring conjecture.