Critical density formula for complete bipartite graphs

Let $K_{n,m}$ be the complete bipartite graph. Denote its critical edge density by $d_{crit}(K_{n,m})=d(n,m)$ and the best edge density obtained from star decomposition by $d_s(n,m)$. Complete bipartite star-decomposition conjecture.

$$d_{crit}(K_{n,m})=d_s(n,m)=1-\frac{1}{n+m-1}.$$

The formula is stated in the complete bipartite graph case, but the source does not provide a resolution status for this conjectural claim.