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Bipartite graph bundles with connected fibres

  • Sungpyo Hong (a1), Jin Ho Kwak (a2) and Jaeun Lee (a3)

Abstract

Let G be a finite connected simple graph. The isomorphism classes of graph bundles and graph coverings over G have been enumerated by Kwak and Lee. Recently, Archdeacon and others characterised bipartite coverings of G and enumerated the isomorphism classes of regular 2p-fold bipartite coverings of G, when G is nonbipartite. In this paper, we characterise bipartite graph bundles over G and derive some enumeration formulas of the isomorphism classes of them when the fibre is a connected bipartite graph. As an application, we compute the exact numbers of the isomorphism classes of bipartite graph bundles over G when the fibre is the path Pn or the cycle Cn.

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Copyright

References

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[1]Archdeacon, D., Kwak, J.H., Lee, J. and Sohn, M.Y., ‘Bipartite covering graphs’, (preprint).
[2]Gross, J.L. and Tucker, T.W., ‘Generating all graph coverings by permutation voltage assignments’, Discrete Math. 18 (1977), 273283.
[3]Gross, J.L. and Tucker, T.W., Topological graph theory (Wiley, New York, 1987).
[4]Hofmeister, M., ‘Counting double covers of graphs’, J. Graph Theory 12 (1988), 437–44.
[5]Kwak, J.H., Chun, J.H. and Lee, J., ‘Enumeration of regular graph coverings having finite abelian covering transformation groups’, SIAM J. Discrete Math. 11 (1998), 273285.
[6]Kwak, J.H. and Lee, J., ‘Isomorphism classes of graph bundles’, Canad. J. Math. 42 (1990), 747761.
[7]Mohar, B., Pisanski, T. and Škoviera, M., ‘The maximum genus of graph bundles’, European J. Combin. 9 (1988), 215224.
[8]Waller, D.A., ‘Double covers of graphs’, Bull. Austral. Math. Soc. 14 (1976), 233248.
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Bipartite graph bundles with connected fibres

  • Sungpyo Hong (a1), Jin Ho Kwak (a2) and Jaeun Lee (a3)

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