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The binary matroids with no $ 4$-wheel minor


Author: James G. Oxley
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
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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.


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DOI: https://doi.org/10.1090/S0002-9947-1987-0879563-6
Article copyright: © Copyright 1987 American Mathematical Society

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