Abstract
The lower bounds on the maximum genus of loopless graphs are obtained according to the connectivity of these graphs. This not only answers a question of Chen, Archdeacon and Gross, but also generalizes the previous known results. Thus, a picture of the lower bounds on the maximum genus of loopless multigraphs is presented.
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References
Kundu, Bounds on number of disjoint spanning trees, J. Combin. Theory Ser. B, 1974, 17: 199–203.
Jungerman, M., A characterization of up-embeddable graphs, Trans. Amer. Math. Soc., 1978, 241: 401–406.
Nebesky, L., A new characterization of the maximum genus of a graph, Czechoslovak Math. J., 1981, 31: 604–613.
Xuong, N. H., How to determine the maximum genus of a graph, J. Combin. Theory Ser. B, 1979, 26: 217–225.
Xuong, N. H., Upper-embeddable graphs and related topics, J. Combin. Theory Ser. B, 1979, 26: 226–232.
Chen, J., Archdeacon, D., Gross, J. L., Maximum genus and connectivity, Discrete Math., 1996, 149: 19–29.
Chen, J., Kanchi, S. P., Gross, J. L., A tight lower bound on the maximum genus of a simplicial graph, Discrete Math., 1996, 156: 83–102.
Gross, J. L., Klein, E. W. and Rieper, R. G., On the average genus of a graph, Graphs and Combinatorics, 1993, 9: 153–162.
Payan, C., Xuong, N. H., Upper embeddability and connectivity of graphs, Discrete Math., 1979, 27: 71–80.
Skoviera, M., The decay number and the maximum genus of a graph, Math. Slovaca., 1992, 42: 391–406.
Cross, J. L. and Tucker, T. W., Topological Graph Theory, Wiley-Interscience, New York, 1987.
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Deming, L., Yanpei, L. Lower bounds on the maximum genus of loopless multigraphs. Appl. Math. Chin. Univ. 15, 359–368 (2000). https://doi.org/10.1007/s11766-000-0031-6
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DOI: https://doi.org/10.1007/s11766-000-0031-6