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Paths and cycles in matroid base graphs

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Abstract

LetG be the base graph of any simple matroid. It is proved thatG is Hamilton-connected, edge-pancyclic, and if for any two vertices ofG there are paths of lengthsm andn joining them,m < n, then there is a path of lengthk joining them for all integersk satisfyingm < k < n.

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References

  1. Bondy, J.A., Ingleton, A.W.: Pancyclic graphs II. J. Comb. Theory (B)20, 41–46 (1976)

    Google Scholar 

  2. Cummins, R.L.: Hamiltonian circuits in tree graphs. IEEE Trans. Circuits Syst.13, 82–90 (1966)

    Google Scholar 

  3. Donald, J.D., Holzmann, C.A., Tobey, M.D.: A characterization of complete matroid base graphs. J. Comb. Theory (B)22, 139–158 (1977)

    Google Scholar 

  4. Holzmann, C.A., Harary, F.: On the tree graph of a matroid. SIAM J. Appl. Math.22, 187–193 (1972)

    Google Scholar 

  5. Maurer, S.B.: Matroid basis graph 1. J. Comb. Theory (B)14, 216–240 (1973)

    Google Scholar 

  6. Welsh, D.J.A.: Matroid Theory. London: Academic Press 1976

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Simon Fraser University, V5A 1S6, Burnaby, B.C., Canada

    Brian Alspach

  2. Institute of Mathematics, Shandong University, Jinan, Shandong, People's Republic of China

    Guizhen Liu

Authors
  1. Brian Alspach
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  2. Guizhen Liu
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Additional information

This research was partially supported by the Natural Sciences and Engineering Council of Canada under Grant A-4792.

This research was done while the author was a Visiting Scholar at Simon Fraser University.

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Alspach, B., Liu, G. Paths and cycles in matroid base graphs. Graphs and Combinatorics 5, 207–211 (1989). https://doi.org/10.1007/BF01788672

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  • DOI: https://doi.org/10.1007/BF01788672

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