Minimum bipartification conjecture for Andrásfai graphs

Let $\textnormal{And}_k$ be the Andrásfai graph, and let $F_k$ be the bipartification defined in Theorem; thus, deleting $F_k$ from $\textnormal{And}_k$ makes it bipartite. Minimum bipartification conjecture. The set $F_k$ defined in Theorem is a minimum bipartification for $\textnormal{And}_k$, meaning that it has the smallest cardinality among bipartifications of $\textnormal{And}_k$. The source presents this as a question the author thinks likely, and gives no resolution.