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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)

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 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.

Keywords

Simple Graph Prime Graph Maximum Cardinality Small Graph Maximum Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Ding, G., Zang, W.: Packing cycles in graphs. J. Combin. Theory Ser. B 86, 381–407 (2003)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Ding, G., Xu, Z., Zang, W.: Packing cycles in graphs, II. J. Combin. Theory Ser. B 87, 244–253 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Edmonds, J., Giles, R.: A min-max relation for submodular functions on graphs. Annals of Discrete Math. 1, 185–204 (1977)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Fulkerson, D.R.: Blocking and anti-blocking pairs of polyhedra. Mathematical Programming 1, 168–194 (1971)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Guenin, B.: Oral communication (2000)Google Scholar
  6. 6.
    Schrijver, A.: Combinatorial Optimization - Polyhedra and Efficiency. Springer, Heidelberg (2003)zbMATHGoogle Scholar

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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