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Stahl, Saul; White, Arthur T.

Genus embeddings for some complete tripartite graphs. (English) Zbl 0322.05105

Discrete Math. 14, 279-296 (1976).
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Cited in 3 Reviews
Cited in 24 Documents

MSC:

05C10 Planar graphs; geometric and topological aspects of graph theory
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References:

[1] Ahlfors, L. V.; Sario, L., Riemann Surfaces (1960), Princeton Univ. Press: Princeton Univ. Press Princeton, N.J · Zbl 0196.33801
[2] S.R. Alpert, Combinatorial representations of polyhedral surfaces, to appear.; S.R. Alpert, Combinatorial representations of polyhedral surfaces, to appear. · Zbl 1220.11011
[3] Behzad, M.; Chartrand, G., Introduction to the Theory of Graphs (1971), Allyn and Bacon: Allyn and Bacon Boston, Mass · Zbl 0177.52403
[4] J.L. Gross, A short proof of Ringel’s bigraph theorem, to appear.; J.L. Gross, A short proof of Ringel’s bigraph theorem, to appear.
[5] Gross, J. L., The genus of nearly complete graphs — case 6, IBM Research Report RC 4302 (April 9, 1973), (#19242)
[6] Gross, J. L., Voltage graphs, Discrete Math., 9, 239-246 (1974) · Zbl 0286.05106
[7] Gross, J. L.; Alpert, S. R., Branched coverings of graph imbeddings, Bull. Am. Math. Soc., 79, 942-945 (1973) · Zbl 0281.05101
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[9] Gross, J. L.; Alpert, S. R., The topological theory of current graphs, J. Combin. Theory, 17, B, 218-233 (1974) · Zbl 0298.05106
[10] J.L. Gross and T.W. Tucker, Quotients of complete graphs: revisiting the Heawood Map- coloring Theorem, to appear.; J.L. Gross and T.W. Tucker, Quotients of complete graphs: revisiting the Heawood Map- coloring Theorem, to appear. · Zbl 0306.55001
[11] G. Haggard, private communication.; G. Haggard, private communication.
[12] Harary, F., Graph Theory (1971), Addison-Wesley: Addison-Wesley Reading, Mass · Zbl 0797.05064
[13] Massey, W. S., Algebraic Topology: An Introduction (1967), Harcourt, Brace and World: Harcourt, Brace and World New York · Zbl 0153.24901
[14] Ringel, G., Das Geschlecht des Vollstāndigen paaren Graphen, Abh. Math. Sem. Univ. Hamburgh, 28, 139-150 (1965) · Zbl 0132.21203
[15] Ringel, G., Der vollstāndige paare Graph auf nichtorientierbaren Flachen, J. Reine Angew. Math., 220, 88-93 (1965) · Zbl 0132.21204
[16] Ringel, G., Map color theorem, Special Session on Advances in Graph Theory, 81st Annual Meeting of the American Mathematical Society in Washington, D.C. (January 25, 1975)
[17] Ringel, G.; Youngs, J. W.T., Das Geschlecht des vollstāndige dreifarbaren Graphen, Comment. Math. Helv., 45, 152-158 (1970) · Zbl 0192.60507
[18] S. Stahl, Generalized embedding schemes, to appear.; S. Stahl, Generalized embedding schemes, to appear. · Zbl 0396.05013
[19] White, A. T., The genus of the complete tripartite graph \(K_{ mn,n,n } \), J. Combin. Theory, 7, 283-285 (1969) · Zbl 0186.27701
[20] White, A. T., The genus of repeated cartesian products of bipartite graphs, Trans. Am. Math. Soc., 151, 393-404 (1970) · Zbl 0202.23401
[21] Youngs, J. W.T., Minimal imbeddings and the genus of a graph, J. Math. Mech., 12, 303-315 (1963) · Zbl 0109.41701
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