7 problems

Let the 35 minor-minimal nonprojective-planar graphs be the graphs described in the preceding discussion, and let $K_1$ denote the graph consisting of a single vertex. Consider the…

Minor-minimal vertex-gluing conjecture. The resulting graph is minor-minimal IPPI3L.

Vertex-gluing conjecture. The resulting graph is IPPI3L.

Two-copy epsilon conjecture. The resulting graph $G$ is minor-minimal IPPI3L.

Epsilon–zeta conjecture. The graph $b5_1$ and every member of the $b6$ family except $b6_3$ are closed nonseparating.

Disjoint-union conjecture. If both $G$ and $H$ are not II3L, then $G\dot{\cup}H$ is minor-minimal IPPI3L.

Weak-separation conjecture. Every member in the $b2$ family is weakly separating.