Bipartification conjecture for homomorphic preimages of Andrásfai graphs

Let $\textnormal{And}_k$ be the Andrásfai graph, and let $H$ be an arbitrary homomorphic preimage of $\textnormal{And}_k$. Let $F_k$ be the bipartification defined in Theorem. Homomorphic-preimage bipartification conjecture. By considering several copies of the bipartification $F_k$, and then optimizing a system of quadratic inequalities, it is possible to prove that $H$ can be made bipartite by deleting at most

$$\frac{1}{25}|H|^2$$

edges. This is described as a special case relevant to the Erdős bipartification conjecture; the source does not provide a proof or resolution.