2 problems

Flat-embedding conjecture. The graph $G$ has a flat embedding precisely when every possible conflict graph is balanced for every maximally planar subgraph $M$. Moreover, if one max…

Let $G$ be a finite simple linklessly embeddable graph with $n$ vertices, where $n\ge 7$, and let $t$ be its number of triangles. McCarty–Thomas conjecture. The graph $G$ has at mo…