Height of minor faces in plane normal maps Original Research Article

The height of a face in a plane graph is the greatest degree of a vertex incident with this face. Under appropriate necessary conditions we prove that any plane normal map has a 3-face of height at most 20, or a 4-face of height at most 11, or else a 5-face of height at most 5. The bounds 20 and 5 are shown to be the best possible.