Intertwining connectivities in representable matroids

Tony Huynh, Stefan H.M. Van Zwam

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Abstract

Let M be a representable matroid and Q,R, S, T subsets of the ground set such that the smallest separation that separates Q from R has order k, and the smallest separation that separates S from T has order l. We prove that if M is sufficiently large, then there is an element e such that in one of M\e and M/e both connectivities are preserved. For matroids representable over a finite field we prove a stronger result: we show that we can remove e such that both a connectivity and a minor of M are preserved.

Original languageEnglish
Pages (from-to)188-196
Number of pages9
JournalSIAM Journal on Discrete Mathematics
Volume28
Issue number1
DOIs
Publication statusPublished - 1 Jan 2014
Externally publishedYes

Keywords

  • Connectivity
  • Intertwining
  • Matroids
  • Tutte s linking theorem

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