2 problems

Let $G$ be a graph, let $A_X(G)$ denote its adjacency matrix with vertex variables, let $\operatorname{mr}_\mathbb{R}(G)$ be the minimum rank of $G$ over $\mathbb{R}$, and let…

Let $\Gamma_{\leq k}$ denote the class of simple graphs with algebraic co-rank at most $k$, and let ${\bf Forb}(\Gamma_{\leq k})$ be the set of graphs that do not contain a graph i…