4 problems

Let $G$ be a graph. Call $G$ intrinsically knotted if every classical spatial embedding of $G$ contains a non-trivial knot, and call it intrinsically virtually knotted of degree 1…

Let $G$ be a planar graph of order at least $11$, and let $\overline{G}$ denote its complement. Intrinsic knotting conjecture. The graph $\overline{G}$ is intrinsically knotted. Th…

Heawood family conjecture. The 20 graphs in the Heawood family are exactly the graphs with 21 edges that are minor minimal with respect to the property of not being 2-apex.

Let $G$ be a bipartite graph with at least five vertices in each part. Write $v(G)=|V(G)|$ for its number of vertices and $e(G)=|E(G)|$ for its number of edges. Intrinsic-knotting…