2 problems

Blowup recolorability conjecture. Every blowup of $G$ is recolorable if and only if every induced subgraph of $G$ is recolorable.

Let $G$ be a graph with $|V(G)|\geq 2$. The prime bound $p(G)$ is the smallest integer such that $G$ admits a prime $p(G)$-extension; here $\alpha(G)$ denotes the stability number…