Maintaining 3-connectivity relative to a fixed basis (2008)
AuthorsOxley, J., Semple, C., Whittle, G.show all
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.
CitationOxley, J., Semple, C., Whittle, G. (2008) Maintaining 3-connectivity relative to a fixed basis. Advances in Applied Mathematics, 41(1), pp. 1-9.
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