Conjecture on the k-coalition number of complete bipartite graphs

Let $K_{s,t}$ be the complete bipartite graph with part sizes $s$ and $t$, where $s\leq t$, and let $C_k(G)$ denote the $k$-coalition number of a graph $G$. Complete bipartite graph coalition conjecture. For $s\leq t$,

$$C_k(K_{s,t})=t-k+2.$$

The paper proves the lower bound $C_k(K_{s,t})\geq t-k+2$ and conjectures that this bound is attained. The equality remains unresolved in the supplied text.