## Abstract

The max-flow min-cut theorem and the two-commodity flow theorem may both be interpreted as equalities between the maximum feasible packing of certain circuits of a graph and the minimum capacity of certain cocircuits, and thus may both be expressed in matroid terms. We study the matroids in which a similar “k-commodity flow theorem” holds. (Thus for k = 1 and 2 it holds for polygon matroids of graphs.) We find for example that such a theorem holds for bond matroids of graphs for all k; and that, for any matroid, if it holds for k = 4, then it holds for all k. We obtain excluded minor characterizations for every k ⩾ 2, and also study the k = 1 case which is still unsolved.

Original language | English (US) |
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Pages (from-to) | 257-290 |

Number of pages | 34 |

Journal | European Journal of Combinatorics |

Volume | 2 |

Issue number | 3 |

DOIs | |

State | Published - 1981 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics