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Half integer extreme points in the linear relaxation of the 2-edge-connected subgraph polyhedron

Author

Listed:
  • F. Bendali

    (Complexe Scientifique des Cézeaux)

  • J. Mailfert

    (Complexe Scientifique des Cézeaux)

Abstract

This paper studies the graphs for which the linear relaxation of the 2-connected spanning subgraph polyhedron has integer or half-integer extreme points. These graphs are called quasi-integer. For these graphs, the linear relaxation of the k-edge connected spanning subgraph polyhedron is integer for all k=4r, r≥1. The class of quasi-integer graphs is closed under minors and contains for instance the class of series-parallel graphs. We discuss some structural properties of graphs which are minimally non quasi-integer graphs, then we examine some basic operations which preserve the quasi-integer property. Using this, we show that the subdivisions of wheels are quasi-integer.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:18:y:2009:i:1:d:10.1007_s10878-007-9134-9
    DOI: 10.1007/s10878-007-9134-9
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    References listed on IDEAS

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    1. Dieter Vandenbussche & George L. Nemhauser, 2005. "The 2-Edge-Connected Subgraph Polyhedron," Journal of Combinatorial Optimization, Springer, vol. 9(4), pages 357-379, June.
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