Straight line representations of planar graphs
The author proves the following modest generalization of what is usually called Fary's theorem. Theorem. Given a planar representation of a graph in which the boundary of each face is a cycle, and given one particular finite face f, there exists an equivalent planar representation in which each edge is represented by a straight line segment and in which the face f forms a convex polygon. The strengthened theorem has the additional advantage that it permits a simplified proof of induction on the number of faces.
scientific article; zbMATH DE number 4150184