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Relations between the Circumference and e-Circumference of a Matroid

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Abstract

For a connected matroid with at least two elements, let c be the maximum size of a circuit and let c e be the maximum size of a circuit that contains an element e. In 2001, Wu prove that \(c_e \ge \left\lceil\frac{c}{2}\right\rceil + 1\). In this note, we characterize the matroids that attain this bound. This characterization is used to generalize another result of Wu.

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References

  1. Junior, B.M.: Connected matroids with a small circumference. Discrete Math. 259, 147–161 (2002)

    Google Scholar 

  2. Lemos, M., Oxley, J.: A sharp bound on the size of a connected matroid. Trans. Amer. Math. Soc. 353, 4039–4056 (2001)

    Google Scholar 

  3. Oxley, J.G.: Matroid Theory. Oxford University Press, New York (1992)

  4. Seymour, P.D.: Decomposition of regular matroids. J. Combin. Theory Ser. B 28, 305–359 (1980)

    Google Scholar 

  5. Tutte, W.T.: Lectures on matroids. J. Res. Nat. Bureau of Standards Ser. B 69, 1–47 (1965)

    Google Scholar 

  6. Wu, P.-L.: On large circuits in matroids, Graphs Combin. 17, 365–388 (2001)

    Google Scholar 

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal de Pernambuco Recife, Pernambuco, 50740-540, Brazil

    Manoel Lemos

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  1. Manoel Lemos
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Correspondence to Manoel Lemos.

Additional information

Manol Lemos: The author is partially supported by CNPq (Grants No. 476224/04-7 and 301178/05-4) and FAPESP/CNPq (Grant No. 2003/09925-5).

Received: October 13, 2006. Final version received: November 6, 2007.

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Lemos, M. Relations between the Circumference and e-Circumference of a Matroid. Graphs and Combinatorics 24, 101–105 (2008). https://doi.org/10.1007/s00373-008-0772-1

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  • DOI: https://doi.org/10.1007/s00373-008-0772-1

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