5 problems

Let $G$ be a finite simple graph and let $\overline{G}$ denote its complement. Let $\mu(G)$ denote the Colin de Verdière parameter. Colin de Verdière's graph complement conjecture.…

Let $G$ be a finite simple graph, let $V(G)$ and $E(G)$ denote its vertex and edge sets, and let $bc(G)$ denote its Colin de Verdière parameter. The Colin de Verdière extremal edge…

Let $G$ be a graph, let $k$ be a positive integer, and let $\mu(G)$ denote the Colin de Verdière parameter of $G$. A graph is generically $k$-stress free if it has no nonzero gener…

Minor characterization conjecture. A signed graph $(G,\Sigma)$ has $\nu(G,\Sigma)\leq 3$ if and only if $(G,\Sigma)$ has no minor isomorphic to $K_5^o$, $K_4^=$, or any signed grap…

Colin de Verdière stress-freeness conjecture. If $\mu(G)\leq k$ for a positive integer $k$, then $G$ is generically $k$-stress free.