\(K_6\)-minors in projective planar graphs
Let \(\Sigma\) be any surface other than the sphere and \(C\) a simple curve of it. The curve \(C\) is called essential if it is not contractible. The face-width of a graph \(G\) embedded in \(\Sigma\) is the minimum number of intersecting points of \(G\) with any essential simple closed curve. It is shown that every 5-connected graph embedded in the projective plane with face-width at least 3 contains the complete graph on 6 vertices as a minor.
scientific article; zbMATH DE number 2099885