A min-max relation on packing feedback vertex sets
Let G be a graph with a nonnegative integral function w defined on V(G). A family 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. In this paper we 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. © Springer-Verlag Berlin Heidelberg 2005.
Publication Source (Journal or Book title)
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Chen, X., Ding, G., Hu, X., & Zang, W. (2005). A min-max relation on packing feedback vertex sets. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 3827 LNCS, 126-135. https://doi.org/10.1007/11602613_14