Two-disjoint-cycle-cover edge bipancyclicity of bipartite generalized hypercubes

Let $G=C(d_1,\dots ,d_n)=F_1\text{BoxProd}\cdots \text{BoxProd}{F}_n$ be a bipartite generalized hypercube with $n\ge 2$, all $d_i$ even, and $N=\mathrm{\mid }V(G)\mathrm{\mid }\ge 8$, where $F_i=K_2$ when $d_i=2$, and $F_i=C_{d_i}$ when $d_i\ge 4$. We prove the following exact strengthening of two-disjoint-cycle-cover vertex bipancyclicity. For every ordered pair of independent edges $e,f\in E(G)$ and every even integer $4\le \mathrm{\ell }\le N-4$, the vertex set can be partitioned into two cycles $J_1,J_2$ of lengths $\mathrm{\ell }$ and $N-\mathrm{\ell }$, respectively, with $e\in E(J_1)$ and $f\in E(J_2)$, if and only if $G$ is not isomorphic to any $K_2\text{BoxProd}{C}_{2p}$ with $p\ge 3$. The graph $C(2,2)\cong C_4$ is treated separately: it has no 2-DCC. Consequences that retain prescribed-edge information include ordinary edge bipancyclicity and the even $k$-ary $n$-cube specialization.