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Generalization of a theorem by V. Eberhard. (English) Zbl 0376.57002

MSC:
57N05 Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010)
57M20 Two-dimensional complexes (manifolds) (MSC2010)
57Q05 General topology of complexes
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References:
[1] BARNETTE D., JUCOVIĆ E., TRENKLER M.: Toroidal maps with prescribed types of vertices and faces. Mathematika 18, 1971, 82-90. · Zbl 0222.05102
[2] EBERHARD V.: Zur Morphologie der Polyeder. Teubner, Leipzig 1891. · JFM 23.0544.03
[3] FISHER J. C: An existence theorem for simple convex polyhedra. Discr. Math. 7, 1974, 75-79. · Zbl 0271.52008
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[12] JUCOVlĆ E., TRENKLER M.: On 4-valent graphs imbedded in orientable 2-manifolds. Studia Sc. Math. Hung. 7, 1972, 225-232. · Zbl 0262.05103
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[14] TRENKLER M.: Planar maps with prescribed degrees of vertices and faces (in Slovak). Acta Fac. Rerum Natur. Univ. Comenian. Math. 32, 1975, 105-118. · Zbl 0329.05111
[15] ZAKS J.: The analogue of Eberhard’s theorem for 4-valent graphs on the torus. Israel J. Math. 9, 1971, 299-305. · Zbl 0222.05103
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