Perfect Matching Interdiction Problem Restricted to a Stable Vertex

  • Gholam Hassan ShirdelEmail author
  • Nasrin Kahkeshani
Original Paper


Suppose v is the stable vertex of a weighted graph G. The purpose of the perfect matching interdiction problem restricted to the stable vertex v in G is to remove v and a vertex adjacent to v such that the weight of the maximum perfect matching in the resulting graph is minimized. In this paper, we present an approximate solution for this problem. According to the approximate and optimal solutions, a special ratio is introduced for this problem. This ratio is not bounded from above and we obtain it for some special classes of graphs.


Perfect matching Interdiction Stable vertex Weighted graph 

Mathematics Subject Classification



  1. 1.
    Akgun, I., Tansel, B.C., Wood, R.K.: The multi-terminal maximum-flow network-interdiction problem. Eur. J. Oper. Res. 211, 241–251 (2011)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Altner, D.S., Ergun, O., Uhan, N.A.: The maximum flow network interdiction problem: valid inequalities, integrality gaps, and approximability. Oper. Res. Lett. 38, 33–38 (2010)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Anandalingam, G., Apprey, V.: Multi-level programming and conflict resolution. Eur. J. Oper. Res. 51, 233–247 (1991)CrossRefGoogle Scholar
  4. 4.
    Assimakopoulos, N.: A network interdiction model for hospital infection control. Comput. Biol. Med. 17, 413–422 (1987)CrossRefGoogle Scholar
  5. 5.
    Corley, H.W., Sha, D.Y.: Most vital links and nodes in weighted network. Oper. Res. Lett. 1, 157–160 (1982)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Israeli, E., Wood, R.K.: Shortest path network interdiction. Networks 40, 97–111 (2002)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Kennedy, K.T., Deckro, R.F., Moore, J.T., Hopkinson, K.M.: Nodal interdiction. Math. Comput. Modell. 54, 3116–3125 (2011)MathSciNetCrossRefGoogle Scholar
  8. 8.
    McMasters, A.W., Mustin, T.M.: Optimal interdiction of a supply network. Nav. Res. Log. Q. 17, 261–268 (1970)CrossRefGoogle Scholar
  9. 9.
    Ratliff, H.D., Sicilia, G.T., Lubore, S.H.: Finding the \(n\) most vital links in flow networks. Manag. Sci. 21, 531–539 (1975)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Wood, R.K.: Deterministic network interdiction. Math. Comput. Modell. 17, 1–18 (1993)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Zenklusen, R.: Matching interdiction. Discrete Appl. Math. 158, 1676–1690 (2010)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Zenklusen, R.: Network flow interdiction on planar graphs. Discrete Appl. Math. 158, 1441–1455 (2010)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature India Private Limited 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Basic SciencesUniversity of QomQomIran

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