Journal of Combinatorial Optimization

, Volume 9, Issue 4, pp 357–379

The 2-Edge-Connected Subgraph Polyhedron

Article

DOI: 10.1007/s10878-005-1777-9

Cite this article as:
Vandenbussche, D. & Nemhauser, G.L. J Comb Optim (2005) 9: 357. doi:10.1007/s10878-005-1777-9

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).

Keywords

network design edge-connectivity traveling salesman problem polyhedra 

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of Mechanical and Industrial EngineeringUniversity of Illinois Urbana-ChampaignUrbana-Champaign
  2. 2.School of Industrial and Systems EngineeringGeorgia Institute of TechnologyUSA