A min-max relation on packing feedback vertex sets

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Conference Proceeding

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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.

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Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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