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Extending Kotzig’s theorem. (English) Zbl 0524.05031

MSC:
05C10 Planar graphs; geometric and topological aspects of graph theory
05C99 Graph theory
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References:
[1] B. Grünbaum,Convex Polytopes, Interscience, New York, 1967.
[2] B. Grünbaum,New views on some old questions of combinatorial geometry, Colloq. Int. Teorie Combinatoire, Rome, 1973, Vol. 1, 1976, pp. 451–468.
[3] B. Grünbaum,Polytopal graphs, inStudies in Graph Theory, part II (D. R. Fulkerson, ed.), Math. Assoc. of America Studies in Math., Vol. 12, 1975, p. 201.
[4] B. Grünbaum and G. C. Shephard,Analogues for tilings of Kotzig’s Theorem on minimal weights of graphs, inTheory and Practice of Combinatorics (A. Rosa, G. Sabidussi and J. Turgeon, eds.), Annals of Discrete Mathematics12 (1982), 129–140. · Zbl 0504.05026
[5] E. Jucovič,Strengthening of a theorem about 3-polytopes, Geom. Dedic.3 (1974), 233–237. · Zbl 0297.52006
[6] A. Kotzig,Príspevok k téorii eulerovských polyédrov, Mat.-Fyz. Časopis Slovensk Akad. Vied.5 (1955), 101–113 (in Slovak; Russian summary).
[7] A. Kotzig,Some open problems and recent results on extremal polyhedral graphs, Publication CRM-796 of C.R.M.A., University of Montreal, 1978; also in Proc. Second Int. Conf. on Combinatorial Mathematics, New York, 1978 (publ. in J. New York Acad. Sci.).
[8] G. Ringel and J. W. T. Young,Solution of the Heawood map coloring problem, Proc. Nat. Acad. Sci. U.S.A.60 (1968), 438–445. · Zbl 0155.51201
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