Packing non-zero A-paths via matroid matching

Shin ichi Tanigawa, Yutaro Yamaguchi

Research output: Contribution to journalArticle

5 Citations (Scopus)

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 languageEnglish
Pages (from-to)169-178
Number of pages10
JournalDiscrete Applied Mathematics
Volume214
DOIs
Publication statusPublished - Jan 1 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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