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Disconnecting graphs by removing vertices: a polyhedral approach

Author

Listed:
  • Maarten Oosten
  • Jeroen H. G. C. Rutten
  • Frits C. R. Spieksma

Abstract

In this paper, we consider the problem of disconnecting a graph by removing as few vertices as possible, such that no component of the disconnected graph has more than a given number of vertices. We give applications of this problem, present a formulation for it, and describe some polyhedral results. Furthermore, we establish ties with other polytopes and show how these relations can be used to obtain facets of our polytope. Finally, we give some computational results.

Suggested Citation

  • Maarten Oosten & Jeroen H. G. C. Rutten & Frits C. R. Spieksma, 2007. "Disconnecting graphs by removing vertices: a polyhedral approach," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 61(1), pages 35-60, February.
    • Handle: RePEc:bla:stanee:v:61:y:2007:i:1:p:35-60
    DOI: 10.1111/j.1467-9574.2007.00350.x
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    Cited by:

    1. Chen, Wei & Jiang, Manrui & Jiang, Cheng & Zhang, Jun, 2020. "Critical node detection problem for complex network in undirected weighted networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    2. Vangerven, Bart & Briskorn, Dirk & Goossens, Dries R. & Spieksma, Frits C.R., 2022. "Parliament seating assignment problems," European Journal of Operational Research, Elsevier, vol. 296(3), pages 914-926.
    3. Ningji Wei & Jose L. Walteros & Foad Mahdavi Pajouh, 2021. "Integer Programming Formulations for Minimum Spanning Tree Interdiction," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1461-1480, October.
    4. Walid Ben-Ameur & Mohamed-Ahmed Mohamed-Sidi & José Neto, 2015. "The $$k$$ k -separator problem: polyhedra, complexity and approximation results," Journal of Combinatorial Optimization, Springer, vol. 29(1), pages 276-307, January.
    5. Alexander Veremyev & Konstantin Pavlikov & Eduardo L. Pasiliao & My T. Thai & Vladimir Boginski, 2019. "Critical nodes in interdependent networks with deterministic and probabilistic cascading failures," Journal of Global Optimization, Springer, vol. 74(4), pages 803-838, August.
    6. Alexander Veremyev & Oleg A. Prokopyev & Eduardo L. Pasiliao, 2014. "An integer programming framework for critical elements detection in graphs," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 233-273, July.
    7. T. N. Dinh & M. T. Thai & H. T. Nguyen, 2014. "Bound and exact methods for assessing link vulnerability in complex networks," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 3-24, July.

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