5 problems

Lovász's finite forcibility conjecture. Finite forcibility is true: the extremal solutions of $t(F,\mathord{\cdot})$ or $I(\mathord{\cdot})$ on…

Let $T(W)$ denote the type space associated with a graphon $W$. Finite-dimensionality conjecture. If $W$ is finitely forcible, then $T(W)$ is finite dimensional. The source intenti…

Let ${\cal W}_0$ be the space of graphons under consideration, and let $T(W)$ denote the type space associated with a graphon $W$. Compactness conjecture. If $W$ is finitely forcib…

Let $F_1,\dots,F_k$ be finite graphs, let $a_1,\dots,a_k$ be prescribed values, and let $t(F_i,W)$ denote the homomorphism density of $F_i$ in a graphon $W$. Finitely forcible solu…

Let $p(x,y)$ be a symmetric polynomial in two variables, and let ${\mathbf 1}_{p(x,y)\ge 0}$ denote its indicator function on $[0,1]^2$. A graphon is a symmetric measurable functio…