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How to determine the maximum genus of a graph. (English) Zbl 0403.05035


MSC:

05C10 Planar graphs; geometric and topological aspects of graph theory
05C35 Extremal problems in graph theory
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References:

[1] Berge, C., (Graphes et Hypergraphes (1973), Dunod: Dunod Paris) · Zbl 0332.05101
[2] Duke, R. A., The genus, regional number and Betti number of graph, Canad. J. Math., 18, 817-822 (1966) · Zbl 0141.21302
[3] Jacques, A., (Thesis (1969), Université de Paris)
[4] Nguyen Huy Xuong; Nguyen Huy Xuong
[5] Nordhaus, E. A.; Stewart, B. M.; White, A. T., On the maximum genus of a graph, J. Combinational Theory Ser. B., 11, 258-267 (1971) · Zbl 0217.02204
[6] Nordhaus, E. A.; Ringeisen, R. D.; Stewart, B. M.; White, A. T., A Kuratowskitype theorem for the maximum genus of a graph, J. Combinatorial Theory Ser. B., 12, 260-267 (1972) · Zbl 0217.02301
[7] Ringeisen, R. D., Upper and lower embeddable graphs, (Graph Theory and Applications (1972), Springer-Verlag: Springer-Verlag New York/Berlin) · Zbl 0559.05053
[8] Ringeisen, R. D., Determining all compact orientable 2-manifold upon which \(K_{m,n}\) has 2-cell imbeddings, J. Combinatorial Theory Ser. B., 12, 101-104 (1972) · Zbl 0213.26002
[9] Ringel, G., Map color theorem (1974), Springer-Verlag: Springer-Verlag New York/Berlin · Zbl 0287.05102
[10] Youngs, J. W.T, Minimal imbeddings and the genus of a graph, J. Math. Mech., 12, 303-316 (1963) · Zbl 0109.41701
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