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The 2EdgeConnected Subgraph Polyhedron
 Dieter Vandenbussche,
 George L. Nemhauser
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We study the polyhedron P(G) defined by the convex hull of 2edgeconnected 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).
 D. Applegate, R. Bixby, V. Chvátal, and W. Cook, “Concorde: A code for solving traveling salesman problems,” http://www.tsp.gatech.edu/concorde.html.
 F. Barahona and A.R. Mahjoub, “On twoconnected subgraph polytopes,” Discrete Math., vol. 147, pp. 19–34, 1995. CrossRef
 S.C. Boyd and W.H. Cunningham, “Small traveling salesman polytopes,” Math. Oper. Res., vol. 16, no. 2, pp. 259–271, 1991.
 S.C. Boyd and T. Hao, “An integer polytope related to the design of survivable communication networks,” SIAM J. Discrete Math., vol. 6, no. 4, pp. 612–630, 1993. CrossRef
 G. Chaty and M. Chein, “Minimally 2edgeconnected graphs,” J. Graph Theory, vol. 3, pp. 15–22, 1979.
 S. Chopra, “The kedgeconnected spanning subgraph polyhedron,” SIAM J. Discrete Math., vol. 7, no. 2, pp. 245–259, 1994. CrossRef
 T. Christof and A. Lóbel, “PORTA: A polyhedron representation transformation algorithm,” http://www.zib.de/Optimization/Software/Porta/, 1997.
 G. Cornuéjols, J. Fonlupt, and D. Naddef, “The travelling salesman problem on a graph and some related integer polyhedra,” Math. Prog., vol. 33, pp. 1–27, 1985. CrossRef
 J. Fonlupt and A.R. Mahjoub, “Critical extreme points of the 2edge connected spanning subgraph polytope,” in Integer Programming and Combinatorial Optimization, volume 1610 of lecture notes in Comput. Sci., Springer, Berlin, 1999, pp. 166–182.
 J. Fonlupt and D. Naddef, “The travelling salesman problem in graphs with some excluded minors,” Math. Prog., vol. 53, no. 2, pp. 147–172, 1992. CrossRef
 M. Grötschel and M.W. Padberg, “On the symmetric travelling salesman problem I: Inequalities,” Math. Prog., vol. 16, no. 3, pp. 265–280, 1979. CrossRef
 M. Grötschel and W.R. Pulleyblank, “Clique tree inequalities and the symmetric travelling salesman problem,” Math. Oper. Res., vol. 11, no. 4, pp. 537–569, 1986.
 M. Grótschel, C.L. Monma, and M. Stoer, “Design of survivable networks,” in Network Models, volume 7 of Handbooks Oper. Res. Management Sci., NorthHolland, Amsterdam, 1995, pp. 617–672.
 A.R. Mahjoub. “Twoedge connected spanning subgraphs and polyhedra,” Math. Prog., vol. 64, no. 2, pp. 199–208, 1994. CrossRef
 A.R. Mahjoub, “On perfectly twoedge connected graphs,” Discrete Math., vol. 170, no. 1–3, pp. 153–172, 1997. CrossRef
 D. Naddef, “The binested inequalities for the symmetric travelling salesman polytope,” Math. Oper. Res., vol. 17, no. 4, pp. 882–900, 1992.
 D. Naddef and G. Rinaldi, “The graphical relaxation: A new framework for the symmetric travelling salesman polytope,” Math. Prog., vol. 58, no. 1, pp. 53–88, 1992. CrossRef
 D. Naddef and S. Thienel, “Efficient separation routines for the symmetric traveling salesman problem. I. general tools and comb separation,” Math. Program., vol. 92 no. 2, Ser. A, pp. 237–255, 2002a. CrossRef
 D. Naddef and S. Thienel, “Efficient separation routines for the symmetric traveling salesman problem. II. Separating multi handle inequalities,” Math. Program., vol. 92, no. 2, Ser. A, 2002b.
 Title
 The 2EdgeConnected Subgraph Polyhedron
 Journal

Journal of Combinatorial Optimization
Volume 9, Issue 4 , pp 357379
 Cover Date
 20050601
 DOI
 10.1007/s1087800517779
 Print ISSN
 13826905
 Online ISSN
 15732886
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 network design
 edgeconnectivity
 traveling salesman problem
 polyhedra
 Industry Sectors
 Authors

 Dieter Vandenbussche ^{(1)}
 George L. Nemhauser ^{(2)}
 Author Affiliations

 1. Department of Mechanical and Industrial Engineering, University of Illinois UrbanaChampaign, UrbanaChampaign
 2. School of Industrial and Systems Engineering, Georgia Institute of Technology, USA