9 problems

Winkler's conjecture. Every simple $n$-Venn diagram can be extended to a simple $(n+1)$-Venn diagram by adding a suitable curve.

Bultena–Ruskey conjecture. Minimum $n$-Venn diagrams exist for all $n\geq 8$.

For an $n$-Venn diagram, consider the graph whose vertices are the crossings of the curves and whose edges are the curve segments between consecutive crossings; this graph may have…

Edge-count upper-bound conjecture.

Edge-number uniqueness conjecture. Every two simple $m$-dimensional $n$-Venn diagrams have the same number of edges.

Fully reducible Venn diagram converse conjecture. If $n\leq m+1$, then $V$ is fully reducible.

Let $\mathcal{F}\subset\mathcal{P}(n)$ be a family of subsets of $[n]$ that contains no $3$-Venn diagram, meaning that there are no sets $A,B,C\in\mathcal{F}$ for which all eight r…

Hamiltonicity conjecture. Every non-simple Venn diagram has a Hamiltonian associated planar graph.

Dihedral-symmetry nonexistence conjecture. There is no simple Venn diagram with dihedral symmetry if $n>3$.