A Min-Max Relation on Packing Feedback Vertex Sets

  • Xujin Chen
  • Guoli Ding
  • Xiaodong Hu
  • Wenan Zang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3827)


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 vV(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.


Simple Graph Prime Graph Maximum Cardinality Small Graph Maximum Edge 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Xujin Chen
    • 1
  • Guoli Ding
    • 2
  • Xiaodong Hu
    • 1
  • Wenan Zang
    • 3
  1. 1.Institute of Applied MathematicsChinese Academy of SciencesBeijingChina
  2. 2.Mathematics DepartmentLouisiana State UniversityBaton RougeUSA
  3. 3.Department of MathematicsThe University of Hong KongHong KongChina

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