The matroids with the max-flow min-cut property

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158 Scopus citations


The max-flow min-cut theorem of Ford and Fulkerson (for undirected networks) may be regarded as a statement about the circuits and cocircuits using some fixed element of the cycle matroid of a graph. We show that, in general, a matroid has this property (in the integer form) if and only if it is binary and has no minor isomorphic to the dual of the Fano matroid.

Original languageEnglish (US)
Pages (from-to)189-222
Number of pages34
JournalJournal of Combinatorial Theory, Series B
Issue number2-3
StatePublished - 1977
Externally publishedYes

All Science Journal Classification (ASJC) codes

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


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