Maintaining 3-connectivity relative to a fixed basis
A standard matrix representation A of a matroid M represents M relative to a fixed basis B. Deleting rows and columns of A correspond to contracting elements of B and deleting elements of E (M) - B. If M is 3-connected, it is often desirable to perform such an element removal from M while maintaining 3-connectivity. This paper proves that this is always possible provided M has no 4-element fans. We also show that, subject to a mild essential restriction, this element removal can be done so as to retain a copy of a specified 3-connected minor of M. © 2007 Elsevier Inc. All rights reserved.
Publication Source (Journal or Book title)
Advances in Applied Mathematics
Oxley, J., Semple, C., & Whittle, G. (2008). Maintaining 3-connectivity relative to a fixed basis. Advances in Applied Mathematics, 41 (1), 1-9. https://doi.org/10.1016/j.aam.2007.05.001