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Edge and vertex operations on upper embeddable graphs. (English) Zbl 0858.05039
A connected graph \(G\) is upper embeddable if the maximum genus of \(G\) is equal to \(\lfloor(|E(G)|-|V(G)|+1)/2\rfloor\). The authors investigate the question of how adding or deleting an edge (or adding one or several vertices) affects upper embeddability. As a consequence, several new classes of upper embeddable graphs are constructed.
05C10 Planar graphs; geometric and topological aspects of graph theory
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[1] BEHZAD M.-CHARTRAD G.-LESNIAK-FOSTER L.: Graphs and Digraphs. Prindle, Weber and Schmidt, Boston, 1979.
[2] FU H. L.-TSAI M. C.: The maximum genus of diameter three graphs. Preprint. · Zbl 0862.05027
[3] JUNGERMAN M.: A characterization of upper embeddable graphs. Trans. Amer. Math. Soc. 241 (1978), 401-406. · Zbl 0379.05025
[4] KUNDU S.: Bounds on the number of disjoint spanning trees. J. Combin. Theory Ser. B 17 (1974), 199-203. · Zbl 0285.05113
[5] NEBESKÝ L.: A new characterization of the maximum genus of a graph. Czechoslovak Math. J. 31(106) (1981), 604-613. · Zbl 0482.05034
[6] NEBESKÝ L.: A note on upper embeddable graphs. Czechoslovak Math. J. 33(108) (1983), 37-40. · Zbl 0518.05029
[7] NEBESKÝ L.: On 2-cell embeddings of graphs with minimum numbers of regions. Czechoslovak Math. J. 35(110) (1985), 625-631. · Zbl 0586.05015
[8] NEDELA R.-ŠKOVIERA M.: The maximum genus of a graph and doubly Eulerian trails. Boll Un. Mat. Ital. B (7) 4 (1990), 541-551. · Zbl 0715.05018
[9] ŠKOVIERA.-M.: The maximum genus of graphs of diameter two. Discrete Math. 87 (1991), 175-180. · Zbl 0724.05021
[10] XUONG N. H.: How to determine the maximum genus of a graph. J. Combin. Theory Ser. B 26 (1979), 217-225. · Zbl 0403.05035
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