Total Dual Integrality of Matching Forest Constraints

G

=(V, E, A) be a mixed graph. That is, (V, E) is an undirected graph and (V, A) is a directed graph. A matching forest (introduced by R. Giles) is a subset F of such that F contains no circuit (in the underlying undirected graph) and such that for each there is at most one such that v is head of e. (For an undirected edge e, both ends of e are called head of e.) Giles gave a polynomial-time algorithm to find a maximum-weight matching forest, yielding as a by-product a characterization of the inequalities determining the convex hull of the incidence vectors of the matching forests. We prove that these inequalities form a totally dual integral system. It is equivalent to an ``all-integer'' min-max relation for the maximum weight of a matching forest. Our proof is based on an exchange property for matching forests, and implies Giles' characterization.

This is a preview of subscription content, access via your institution.

Author information

Affiliations

Authors

Additional information

Received August 31, 1998

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Schrijver, A. Total Dual Integrality of Matching Forest Constraints. Combinatorica 20, 575–588 (2000). https://doi.org/10.1007/s004930070009

Download citation

  • AMS Subject Classification (1991) Classes:  05C70, 90C27, 90C57