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The 2-Edge-Connected Subgraph Polyhedron

Author

Listed:
  • Dieter Vandenbussche

    (University of Illinois Urbana-Champaign)

  • George L. Nemhauser

    (Georgia Institute of Technology)

Abstract

We study the polyhedron P(G) defined by the convex hull of 2-edge-connected subgraphs of G where multiple copies of edges may be chosen. We show that each vertex of P(G) is also a vertex of the LP relaxation. Given the close relationship with the Graphical Traveling Salesman problem (GTSP), we examine how polyhedral results for GTSP can be modified and applied to P(G). We characterize graphs for which P(G) is integral and study how this relates to a similar result for GTSP. In addition, we show how one can modify some classes of valid inequalities for GTSP and produce new valid inequalities and facets for P(G).

Suggested Citation

  • Dieter Vandenbussche & George L. Nemhauser, 2005. "The 2-Edge-Connected Subgraph Polyhedron," Journal of Combinatorial Optimization, Springer, vol. 9(4), pages 357-379, June.
    • Handle: RePEc:spr:jcomop:v:9:y:2005:i:4:d:10.1007_s10878-005-1777-9
    DOI: 10.1007/s10878-005-1777-9
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    References listed on IDEAS

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    1. Sylvia C. Boyd & William H. Cunningham, 1991. "Small Travelling Salesman Polytopes," Mathematics of Operations Research, INFORMS, vol. 16(2), pages 259-271, May.
    2. M. Grötschel & W. R. Pulleyblank, 1986. "Clique Tree Inequalities and the Symmetric Travelling Salesman Problem," Mathematics of Operations Research, INFORMS, vol. 11(4), pages 537-569, November.
    3. Denis Naddef, 1992. "The Binested Inequalities for the Symmetric Traveling Salesman Polytope," Mathematics of Operations Research, INFORMS, vol. 17(4), pages 882-900, November.
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    Cited by:

    1. Oya Ekin Karaşan & A. Ridha Mahjoub & Onur Özkök & Hande Yaman, 2014. "Survivability in Hierarchical Telecommunications Networks Under Dual Homing," INFORMS Journal on Computing, INFORMS, vol. 26(1), pages 1-15, February.
    2. F. Bendali & J. Mailfert, 2009. "Half integer extreme points in the linear relaxation of the 2-edge-connected subgraph polyhedron," Journal of Combinatorial Optimization, Springer, vol. 18(1), pages 1-22, July.

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