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On the Circuit-cocircuit Intersection Conjecture

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Abstract

Oxley has conjectured that for k≥4, if a matroid M has a k-element set that is the intersection of a circuit and a cocircuit, then M has a (k−2)-element set that is the intersection of a circuit and a cocircuit. In this paper we prove a stronger version of this conjecture for regular matroids. We also show that the stronger result does not hold for binary matroids.

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References

  1. Kingan, S. R.: Intersections of circuits and cocircuits in binary matroids, Discrete Math. 195, 157–165 (1999)

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  2. Oxley, J. G.: On the intersections of circuits and cocircuits in matroids, Combinatorica 4, 187–195 (1984)

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

  4. Seymour, P. D.: The forbidden minors of binary clutters. J. London Math. Soc. 12(2), 356–360 (1976)

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

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Clayton State University, Morrow, GA, 30260

    S. R. Kingan

  2. Departamento de Matematica, Universidade Federal de Pernambuco, Recife, Pernambuco, 50740-540, Brazil

    Manoel Lemos

Authors
  1. S. R. Kingan
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  2. Manoel Lemos
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Corresponding author

Correspondence to S. R. Kingan.

Additional information

The second author was partially supported by CNPq (grant no 302195/02-5) and the ProNEx/CNPq (grant no 664107/97-4).

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Kingan, S., Lemos, M. On the Circuit-cocircuit Intersection Conjecture. Graphs and Combinatorics 22, 471–480 (2006). https://doi.org/10.1007/s00373-006-0680-1

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  • DOI: https://doi.org/10.1007/s00373-006-0680-1

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