## The binary matroids with no $4$-wheel minor

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- by James G. Oxley
- Trans. Amer. Math. Soc.
**301**(1987), 63-75 - DOI: https://doi.org/10.1090/S0002-9947-1987-0879563-6
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## Abstract:

The cycle matroids of wheels are the fundamental building blocks for the class of binary matroids. Brylawski has shown that a binary matroid has no minor isomorphic to the rank-3 wheel $M({\mathcal {W}_3})$ if and only if it is a series-parallel network. In this paper we characterize the binary matroids with no minor isomorphic to $M({\mathcal {W}_4})$. This characterization is used to solve the critical problem for this class of matroids and to extend results of Kung and Walton and Welsh for related classes of binary matroids.## References

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## Bibliographic Information

- © Copyright 1987 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**301**(1987), 63-75 - MSC: Primary 05B35; Secondary 05C75
- DOI: https://doi.org/10.1090/S0002-9947-1987-0879563-6
- MathSciNet review: 879563