Abstract
In this paper, on the basis of joint tree model introduced by Liu, by dividing the associated surfaces into segments layer by layer, we show that there are at least \({C_{1}\cdot C_{2}^{\frac{m}{2}}\cdot C_{3}^{\frac{n}{2}}(m-1)^{m-\frac{1}{2}}(n-1)^{n-\frac{1}{2}}}\) distinct genus embeddings for complete bipartite graph K m,n , where C 1, C 2, and C 3 are constants depending on the residual class of m modular 4 and that of n modular 4.
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Shao, Z., Liu, Y. & Li, Z. On the Number of Genus Embeddings of Complete Bipartite Graphs. Graphs and Combinatorics 29, 1909–1919 (2013). https://doi.org/10.1007/s00373-012-1227-2
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DOI: https://doi.org/10.1007/s00373-012-1227-2