TY - JOUR

T1 - Packing non-zero A-paths via matroid matching

AU - Tanigawa, Shin ichi

AU - Yamaguchi, Yutaro

N1 - Funding Information:
The first author is supported by JSPS KAKENHI Grant Number 15K15942 . The second author was supported by JSPS Grant-in-Aid for JSPS Fellows (Grant Number 13J02522 ) during this work.
Publisher Copyright:
© 2016 Elsevier B.V.

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84977675563&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84977675563&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2016.06.001

DO - 10.1016/j.dam.2016.06.001

M3 - Article

AN - SCOPUS:84977675563

VL - 214

SP - 169

EP - 178

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -