Wang–Qin–Xia's stability conjecture for nontrivial graph pairs

Let $(\Gamma,\Sigma)$ be a nontrivial graph pair, meaning that $\Gamma$ and $\Sigma$ are coprime connected twin-free graphs and exactly one of them is bipartite. Assume that the graphs have no loops and that $\Sigma$ is bipartite. Wang–Qin–Xia's conjecture. The pair $(\Gamma,\Sigma)$ is stable if and only if $\Gamma$ is stable. This conjecture asks when stability of a nontrivial graph pair reduces to stability of its non-bipartite factor; the supplied source gives no resolution, so the conjecture remains open.