5 problems

De Klerk–Pasechnik conjecture. For every non-empty graph $G$,

Let $G$ be a graph with stability number $\alpha(G)$, and let $A_G$, $I$, and $J$ denote its adjacency, identity, and all-ones matrices, respectively. Define … By the Motzkin–Strau…

Finite-termination conjecture. For $A\notin{\mathcal{CP}}^n$, Procedure with a suitable pivot rule in Step2(b) ends after finitely many iterations with a separating witness $W$.

Forbidden-subgraph characterization conjecture. The list of graphs in Theorem is a complete list of forbidden subgraphs for the property of being SPN.

Subdivision conjecture for $K_4$. Every subdivision of $K_4$ in which all six edges were subdivided, each at least once, is SPN.