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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The binary matroids with no $4$-wheel minor
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by James G. Oxley PDF
Trans. Amer. Math. Soc. 301 (1987), 63-75 Request permission

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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Additional 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