2 problems

Let $G=(V,E)$ be a graph, let $\vartheta^{(r)}(G)$ be its order-$r$ copositive hierarchy bound, and let $S^\perp$ denote the vertices adjacent to or equal to a stable set $S$. For…

Let $G$ be a graph, let $M_G$ be its graph matrix, let $F_G(x)=(x^{\circ2})^TM_Gx^{\circ2}$, and let … Define $\vartheta^{(r)}(G)=\min\{t:t(A_G+I)-J\in\mathcal K_n^{(r)}\}$. The fi…