On minor-minimally 3-connected binary matroids

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Abstract

A matroid M is called minor-minimally 3-connected if M is 3-connected and, for each e ∈ E (M), either M {set minus} e or M / e is not 3-connected. In this paper, we prove a chain theorem for the class of minor-minimally 3-connected binary matroids. As a consequence, we obtain a chain theorem for the class of minor-minimally 3-connected graphs. © 2008 Elsevier B.V. All rights reserved.

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Delaplane, L., Reid, T. J., Wu, H., & Zhou, X. (2009). On minor-minimally 3-connected binary matroids. Discrete Mathematics, 309(10), 3249–3254. https://doi.org/10.1016/j.disc.2008.09.027

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