We prove that, for each nonnegative integer k and each matroid N, if M is a 3-connected matroid containing N as a minor, and the the branch width of M is sufficiently large, then there is a k-element subset X of E(M) such that one of M\X and M/X is 3-connected and contains N as a minor.
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Cornell University Library
arXiv.org e-Print archive
Matroid Structure for Efficiency
Networks and Optimization

van Zwam, S.H.M, & Geelen, J. (2011). Matroid 3-connectivity and branch width. arXiv.org e-Print archive. Cornell University Library .