Proof of a conjecture of Kahn for non-binary matroids

Abstract

This note proves a conjecture of Kahn by showing that ifX is a 3-element independent set in a 3-connected non-binary matroid M, thenM has a connected non-binary minor havingX as a basis.

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References

  1. [1]

    R. E. Bixby,l-matrices and a characterization of binary matroids,Discrete Math. 8 (1974), 139–145.

    MATH  Article  MathSciNet  Google Scholar 

  2. [2]

    T. Inukai andL. Weinberg, Theorems on matroid connectivity,Discrete Math. 22 (1978), 311–312.

    MATH  Article  MathSciNet  Google Scholar 

  3. [3]

    J. Kahn, A problem of P. Seymour on nonbinary matroids,Combinatorica 5 (1985), 319–323.

    MATH  MathSciNet  Google Scholar 

  4. [4]

    J. G. Oxley, On non-binary 3-connected matroids,Trans. Amer. Math. Soc., to appear.

  5. [5]

    W. R. H. Richarson, Decomposition of chain groups and binary matroids, in:Proc. Fourth Southeastern Conf. on Combinatorics, Graph Theory and Computing (Utilitas Mathematica, Winnipeg, 1973), 463–476.

    Google Scholar 

  6. [6]

    P. D. Seymour, On minors of non-binary matroids,Combinatorica 1 (1981), 387–394.

    MATH  MathSciNet  Google Scholar 

  7. [7]

    P. D. Seymour, Triples in matroid circuits,to appear.

  8. [8]

    D. J. A. Welsh,Matroid Theory, Academic Press, London, New York, San Francisco, 1976.

    Google Scholar 

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This research was partially supported by an LSU Summer Research Grant.

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Oxley, J.G. Proof of a conjecture of Kahn for non-binary matroids. Combinatorica 5, 343–345 (1985). https://doi.org/10.1007/BF02579249

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AMS subject classification (1980)

  • 05 B 35