The prescribed partition conjecture for disjoint cycles in bipartite graphs

Let $G[X,Y]$ be a balanced bipartite graph of order $2n$, let $S$ be a subset of $X$ with $|S|\geq 2k+2$, and let $S_{C_i}$ denote the vertices of $S$ on a cycle $C_i$. Prescribed partition conjecture. If

$$\sigma_{1,1}(S)\geq n+2,$$

then for any integer partition

$$|S|=n_1+\cdots+n_k,\qquad n_i\geq 2\quad(1\leq i\leq k),$$

there are $k$ disjoint cycles $C_1,\ldots,C_k$ such that

$$|S_{C_i}|=n_i\quad\text{for all }1\leq i\leq k.$$

This is a stronger prescribed-distribution version of the cycle-covering problem: the degree-sum condition is required to realize every partition of the specified vertices into admissible cycle sizes. The supplied text gives no resolution, so the conjecture remains open.