A min-max relation on packing feedback vertex sets

  • Authors:

  • Xujin Chen;Guoli Ding;Xiaodong Hu;Wenan Zang

  • Affiliations:

  • Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, China;Mathematics Department, Louisiana State University, Baton Rouge, Louisiana;Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, China;Department of Mathematics, The University of Hong Kong, Hong Kong, China

  • Venue:
  • ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
  • Year:
  • 2005

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Abstract

Let G be a graph with a nonnegative integral function w defined on V(G). A family $\mathcal{F}$ of subsets of V(G) (repetition is allowed) is called a feedback vertex set packing in G if the removal of any member of $\mathcal{F}$ from G leaves a forest, and every vertex v∈ V(G) is contained in at most w(v) members of $\mathcal{F}$. 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.