#### Title

A min-max relation on packing feedback vertex sets

#### Document Type

Article

#### Publication Date

11-1-2006

#### Abstract

Let G be a graph with a nonnegative integral function w defined on V(G). A collection f of subsets of V(G) (repetition is allowed) is called a feedback vertex set packing in G if the removal of any member of f from G leaves a forest, and every vertex v ∈ V(G) is contained in at most w(v) members of f The weight of a cycle C in G is the sum of w(v), over all vertices v of C. The purpose of this paper is to characterize all graphs with the property that, for any nonnegative integral function w, the maximum cardinality of a feedback vertex set packing is equal to the minimum weight of a cycle. © 2006 INFORMS.

#### Publication Source (Journal or Book title)

Mathematics of Operations Research

#### First Page

777

#### Last Page

788

#### Recommended Citation

Chen, X., Ding, G., Hu, X., & Zang, W.
(2006). A min-max relation on packing feedback vertex sets.* Mathematics of Operations Research**, 31* (4), 777-788.
https://doi.org/10.1287/moor.1060.0200