The binary matroids with no 4-wheel minor

Document Type

Article

Publication Date

1-1-1987

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(W3) if and only if it is a series-parallel network. In this paper we characterize the binary matroids with no minor isomorphic to M(W4). 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. © 1987 American Mathematical Society.

Publication Source (Journal or Book title)

Transactions of the American Mathematical Society

First Page

63

Last Page

75

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