Abstract
Let G = (V, E) be an oriented graph whose edges are labelled by the elements of a group Γ and let A ⊆ V. An A-path is a path whose ends are both in A. The weight of a path P in G is the sum of the group values on forward oriented arcs minus the sum of the backward oriented arcs in P. (If Γ is not abelian, we sum the labels in their order along the path.) We give an efficient algorithm for finding a maximum collection of vertex-disjoint A-paths each of non-zero weight. When A = V this problem is equivalent to the maximum matching problem.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. Chudnovsky, J. Geelen, B. Gerards, L. Goddyn, M. Lohman and P. Seymour: Packing non-zero A-paths in group-labelled graphs, Combinatorica 26(5) (2006), 521–532.
L. Lovász: Matroid matching and some applications, J. Combin. Theory Ser. B 28 (1980), 208–236.
L. Lovász and M. D. Plummer: Matching Theory, North-Holland, 1986.
W. Mader: Über die Maximalzahl kreuzungsfreier H-Wege, Archiv der Mathematik (Basel) 31 (1978), 382–402.
A. Sebő and L. Szegő: The path-packing structure of graphs, in: Integer Programming and Combinatorial Optimization (Proceedings 10th IPCO Conference, New York, 2004; D. Bienstock, G. Nemhauser, eds.) [Lecture Notes in Computer Science 3064], Springer, Berlin, 2004, pp. 256–270.
Author information
Authors and Affiliations
Additional information
This research was partially conducted during the period Chudnovsky served as a Clay Mathematics Institute Long-Term Prize Fellow. The research was supported in part by the Natural Sciences and Engineering Council of Canada.
Rights and permissions
About this article
Cite this article
Chudnovsky, M., Cunningham, W.H. & Geelen, J. An algorithm for packing non-zero A-paths in group-labelled graphs. Combinatorica 28, 145–161 (2008). https://doi.org/10.1007/s00493-008-2157-8
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00493-008-2157-8