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Orientably simple graphs. (English) Zbl 0643.05027
In 1963 J. W. T. Youngs has shown that minimal embeddings of connected graphs are necessarily 2-cell embeddings. The authors give necessary and sufficient conditions for a nonorientable analog of Youngs’ theorem.
Reviewer: V.Peteanu

MSC:
05C10 Planar graphs; geometric and topological aspects of graph theory
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References:
[1] AUSLANDER L., BROWN T. A., YOUNGS J. W. T.: The imbedding of a graph in manifolds. J. Math. Mech. 12, 1963, 629-634. · Zbl 0115.40804
[2] FRANKLIN P.: A six color problem. J. Math. and Phys. 13, 1934, 363-369. · Zbl 0010.27502
[3] RINGEL G.: The combinatorial map color theorem. J. Graph. Theory 1, 1977, 141-155. · Zbl 0386.05030
[4] RINGEL G.: Non-existence of graph embeddings. (in Theory and Applications of Graphs, Proceedings, Y. Alavi and D. R. Lick, LNM 642, Springer-Verlag, New York 1978, 465-476. · Zbl 0398.05031
[5] STAHL S.: Generalized embedding schemes. J. Graph Theory 2, 1978, 41-52. · Zbl 0396.05013
[6] STAHL S., BEINEKE L. W.: Blocks and the nonorientable genus of a graph. J. Graph Theory 1, 1977, 75-78. · Zbl 0366.05030
[7] WHITE A. T.: Graphs, Groups and Surfaces. North Holland, London, 1984. · Zbl 0551.05037
[8] WHITE A. T., BEINEKE L. W.: Topological graph theory. (in Selected Topics in Graph Theory), L. W. Beineke and R. J. Wilson, Academic Press, London 1978, 15-50. · Zbl 0439.05018
[9] YOUNGS J. W. T.: Minimal imbeddings and the genus of a graph. J. Math. Mech. 12, 1963, 303-315. · Zbl 0109.41701
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