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The analogue of Eberhard’s theorem for 4-valent graphs on the torus. (English) Zbl 0222.05103

MSC:
05C10 Planar graphs; geometric and topological aspects of graph theory
52B05 Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.)
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References:
[1] D. Barnette, (to appear).
[2] V. Eberhard,Zur Morphologie der Polyeder, Teunber, Leipzig, 1891.
[3] B. Grünbaum,Convex Polytopes, J. Wiley and Sons, New York, 1967. · Zbl 0163.16603
[4] B. Grünbaum,Some analogues of Eberhard’s Theorem on Convex Polytopes, Israel J. Math.6 (1968), 398–411. · Zbl 0174.53702
[5] B. Grünbaum,Planar maps with prescribed types of vertices and faces, Mathematika16 (1969), 28–36. · Zbl 0186.27502
[6] E. Jucovič, (to appear).
[7] E. Steinitz,Polyeder und Raumeinteilungen, Enzykl, Math. Wiss, Vol. 3 (Geometrie) Part 3AB12, pp. 1–139, 1922.
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