Concentric Bilinski diagrams.
Jennifer Antoinette Bruce, Mark E. Watkins · 2004
A Bilinski diagram (respectively, B ∗-diagram) is a labeling of a planar map with respect to the regional distance of its vertices and faces from a central vertex (respectively, face). Such diagrams are concentric if for each k ≥ 1, the set of vertices at regional distance k from the central vertex or face induces a circuit. The class Ga,b consists of all 1-ended, 3-connected planar maps with the property that every valence is finite and at least a and every covalence is finite and at least b. Amapinthe subclass Ga,b+ of Ga,b contains no adjacent b-covalent faces, and dually a map in Ga+,b contains no adjacent a-valent vertices. It is shown that all