### Abstract

A Γ-labeled graph is a directed graph G in which each edge is associated with an element of a group Γ by a label function ψ:E(G)→Γ. For a vertex subset A⊆V(G), a path (in the underlying undirected graph) is called an A-path if its start and end vertices belong to A and does not intersect A in between, and an A-path is called non-zero if the ordered product of the labels along the path is not equal to the identity of Γ. Chudnovsky et al. (2006) introduced the problem of packing non-zero A-paths and gave a min–max formula for characterizing the maximum number of vertex-disjoint non-zero A-paths. In this paper, we show that the problem of packing non-zero A-paths can be reduced to the matroid matching problem on a certain combinatorial matroid, and discuss how to derive the min–max formula based on Lovász’ idea of reducing Mader's S-paths problem to matroid matching.

Original language | English |
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Pages (from-to) | 169-178 |

Number of pages | 10 |

Journal | Discrete Applied Mathematics |

Volume | 214 |

DOIs | |

Publication status | Published - Jan 1 2016 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Applied Mathematics

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## Cite this

*Discrete Applied Mathematics*,

*214*, 169-178. https://doi.org/10.1016/j.dam.2016.06.001