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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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[1] BARNETTE D., JUCOVIĆ E., TRENKLER M.: Toroidal maps with prescribed types of vertices and faces. Mathematika 18, 1971, 82-90. · Zbl 0222.05102 · doi:10.1112/S0025579300008408
[2] EBERHARD V.: Zur Morphologie der Polyeder. Teubner, Leipzig 1891. · JFM 23.0544.03
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[4] GRÜNBAUM B.: Convex Polytopes. Interscience, New York 1967. · Zbl 0163.16603
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[10] JENDROL’ S., JUCOVIĆ E.: On the toroidal analogue of Eberhard’s theorem. Proc. London Math. Soc. 25, 1972, 385-398. · Zbl 0239.05107 · doi:10.1112/plms/s3-25.3.385
[11] JUCOVlĆ E.: Analogues of Eberhard’s theorem for 4-valent 3-polytopes with involutory automorphisms. Discr. Math. 6, 1973, 249-254, · Zbl 0265.52006 · doi:10.1016/0012-365X(73)90097-6
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[13] JUCOVlĆ E., TRENKLER M.: A theorem on the structure of cell-decompositions of orientable 2-manifolds. Mathematika 20, 1973, 63-82. · Zbl 0273.57005 · doi:10.1112/S0025579300003648
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[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 · doi:10.1007/BF02771680
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[17] ZAKS J.: 6-valent analogues of Eberhard’s theorem. Israel J. Math. 18, 1974, 19-29. · Zbl 0291.05102 · doi:10.1007/BF02758126
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