[PDF] Embedding Planar Graphs at Fixed Vertex Locations | Semantic Scholar

It is shown that any graph of n vertices that can be drawn in the plane with no k+1 pairwise crossing edges has at most c-c-k-n log 2-supscrpt-−2 edges, which gives a partial answer to a dual version of a well-known problem of Avital-Hanani, Erdo&huml;s, Kupitz, Perles, and others.