Babu–Diwan-type subdivision conjecture for vertex-disjoint even cycles

Let $H$ be a graph of order $n$ with $k$ components, each of which is an even cycle. Let $G$ be a bipartite graph with bipartition $(X,Y)$ such that

$$|X|=|Y|\geq n/2.$$

Subdivision conjecture. If the minimum degree of $G$ is at least $n/2-k+1$, then $G$ contains a subdivision of $H$.

This conjecture extends the preceding theorem, which proves the same assertion when every cycle has length at least $6$, and includes the vertex-disjoint-cycle result as a special case. The statement concerns the degree threshold guaranteeing subdivisions of graphs whose components are even cycles.