Packing and covering with matroid circuits

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Abstract

We prove a conjecture of Welsh, that for every matroid M without coloops, ν(M) + θ(M) ≤ ρ{variant}(M) + κ(M) where ν(M) is the maximum number of pairwise disjoint circuits, θ(M) is the minimum number of circuits whose union is E(M), ρ{variant}(M) is the corank of M, and κ(M) is the number of connected components of M. For binary matroids the result was previously proved by Oxley.

Original languageEnglish (US)
Pages (from-to)237-242
Number of pages6
JournalJournal of Combinatorial Theory, Series B
Volume28
Issue number2
DOIs
StatePublished - Apr 1980
Externally publishedYes

All Science Journal Classification (ASJC) codes

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

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