3 problems

Basic semialgebraicity conjecture. The set of spectra realizable by symmetric nonnegative matrices forms a basic semi-algebraic set.

Let $G$ and $H$ be graphs such that $q(G)=q(H)=2$, with $MB(G)=k_1$ and $MB(H)=k_2$, and suppose that the quantities denoted in the source by $\mrr+(G)$ and $\mrr+(H)$ satisfy…

Let $T=S^k_{m,n}$ be the tree formed by taking a path on $k$ vertices and adding $m$ leaves to one endpoint and $n$ leaves to the other, where $kin\{2,3,4\}$ and $m,n>1$. Write…