On the connectivity function of a matroid

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Abstract

The connectivity function k of a matroid M on a set E is defined by k(X) = r(X) + r(E - X) - r(E) (X ⊆ E), where r is the rank function. W. H. Cunningham conjectured that a connected matroid is determined, up to duality, by a knowledge of its connectivity function. This is false in general, but true for binary matroids.

Original languageEnglish (US)
Pages (from-to)25-30
Number of pages6
JournalJournal of Combinatorial Theory, Series B
Volume45
Issue number1
DOIs
StatePublished - Aug 1988
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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