3 problems

The positive graph conjecture. A graph $H$ is positive if and only if it has a stable involution.

Let $F$ be a bipartite graph, and let $\mathrm{E}^r(F)$ denote its $r$-uniform expansion: each edge of $F$ is extended to an $r$-edge by adding new vertices. An $r$-graph is Sidore…

Let $H$ be an $r$-uniform hypergraph, or $r$-graph. Call $H$ positive when its corresponding hypergraph homomorphism-density functional is nonnegative for every bounded measurable…