Decomposition of binary matroids


We prove results relating to the decomposition of a binary matroid, including its uniqueness when the matroid is cosimple. We extend the idea of “freedom” of an element in a matroid to “freedom” of a set, and show that there is a unique maximal integer polymatroid inducing a given binary matroid.

This is a preview of subscription content, access via your institution.


  1. [1]

    W. H. Cunningham, Binary matroid sums,Quart. J. Math. Oxford (2),30 (1979), 271–281.

    MATH  Article  MathSciNet  Google Scholar 

  2. [2]

    J. E. Dawson, Balanced sets in an independence structure induced by a submodular function,J. Math. Anal. Appl.,95 (1983), 214–222.

    MATH  Article  MathSciNet  Google Scholar 

  3. [3]

    J. E. Dawson, Solubility of the matroid sum equation,Ars Combinatoria,17A (1984), 103–116.

    Google Scholar 

  4. [4]

    R. Duke,Freedom in matroids, Ph. D. thesis, Open University, 1981.

  5. [5]

    L. Lovász andA. Recski, On the sum of matroids,Acta Math. Acad. Sci. Hung.,24 (1972), 329–333.

    Article  Google Scholar 

  6. [6]

    H. Q. Nguyen, Semimodular functions and combinatorial geometries,Trans. Amer. Math. Soc.,238 (1978), 355–383.

    MATH  Article  MathSciNet  Google Scholar 

  7. [7]

    J. S. Pym andHazel Perfect, Submodular functions and independence structures,J. Math. Anal., Appl.,30 (1970), 1–31.

    MATH  Article  MathSciNet  Google Scholar 

  8. [8]

    A. Recski, On the sum of matroids, III,Discrete Math.,36 (1981), 273–287.

    MATH  Article  MathSciNet  Google Scholar 

  9. [9]

    A. Recski, Some open problems of matroid theory, suggested by its applications,Proc. Matroid Theory Conference, Szeged, Hungary, (1982),to appear.

Download references

Author information



Rights and permissions

Reprints and Permissions

About this article

Cite this article

Dawson, J.E. Decomposition of binary matroids. Combinatorica 5, 1–9 (1985).

Download citation

AMS subject classification (1980)

  • 05 B 35