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.
Additional Metadata
Keywords Matroids, Connectivity, Branch width, Tangles, Splitter theorem
MSC Matroids, geometric lattices (msc 05B35)
THEME Other (theme 6)
Publisher Academic Press
Persistent URL dx.doi.org/10.1016/j.jctb.2014.12.003
Journal Journal of Combinatorial Theory - Series B
Project Matroid Structure for Efficiency
Citation
van Zwam, S.H.M, & Geelen, J. (2015). Matroid 3-connectivity and branch width. Journal of Combinatorial Theory - Series B, 112(0), 104–123. doi:10.1016/j.jctb.2014.12.003