Signed diagonal flips and the four color theorem
A flip of a diagonal \(e=uw\) in a plane triangulation \(T\) removes \(e\) from the quadrilateral \(uvwxu\) formed by the two faces of \(T\) adjacent to \(e\) and adds the opposite diagonal \(vx\). The author introduces a signed version of this operation, conjectures that any two triangulations of a given polygon can be transformed into each other by a signable sequence of diagonal flips, and shows that the conjectured statement would imply the four color theorem.
scientific article; zbMATH DE number 1382656
scientific article