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Polytopal graphs. (English) Zbl 0678.05015
Selected topics in graph theory, Vol. 3, 169-188 (1988).
[For the entire collection see Zbl 0648.00003.]
This is a survey paper of several areas in the study of polytopal graphs. A graph is d-polytopal if it is the graph formed by the vertices and edges of a d-dimensional convex polytope. The 3-polytopal graphs are exactly the 3-connected planar graphs. The topics surveyed in most depth are the realizability of sets of face sizes, and the existence of cycles and paths, especially hamiltonian cycles.
Reviewer: B.McKay

MSC:
05C10 Planar graphs; geometric and topological aspects of graph theory
05C45 Eulerian and Hamiltonian graphs
52Bxx Polytopes and polyhedra
51M20 Polyhedra and polytopes; regular figures, division of spaces
05-02 Research exposition (monographs, survey articles) pertaining to combinatorics
52-02 Research exposition (monographs, survey articles) pertaining to convex and discrete geometry