Geodesic
Bi-embeddings of graphs
Glasgow mathematical journal, Tome 15 (1974) no. 2, pp. 162-165

Voir la notice de l'article provenant de la source Cambridge University Press

Let γ and γ' be non-negative integers. We say that the graph G is (γ, γ') bi-embeddable if G can be embedded in a surface of genus γ and the complement Ḡ of G can be embedded in a surface of genus γ'. Let N(γ, γ') be the least integer such that every graph with at least N(γ, γ') points is not (γ, γ') bi-embeddable. It has been shown in [1] and [5] that N(0, 0) = 9; this result was also obtained by John R. Ball of the Carnegie Institute of Technology. Our object here is to obtain upper and lower bounds for N(γ, γ'). 
Anderson, I.; Cook, R. J. Bi-embeddings of graphs. Glasgow mathematical journal, Tome 15 (1974) no. 2, pp. 162-165. doi: 10.1017/S0017089500002354
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