3 problems

Strong local Brandt–Thomassé conjecture. There exists a finite set $U$ with

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. Homo…

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…