Polyhedral Results for 1-Restricted Simple 2-Matchings
David Hartvigsen, Yanjun Li · SIAM Journal on Optimization · 2008
A simple 2-matching in a graph is a subgraph whose connected components are nontrivial paths and cycles. A simple 2-matching is called 1-restricted if each connected component has two or more edges. In this paper we consider the problem of finding maximum weight 1-restricted simple 2-matchings (which is a relaxation of the traveling salesman problem). We present an integer programming formulation for this problem, characterize the extreme points of the linear programming relaxation, and characterize the graphs for which the linear programming relaxation has all integral extreme points. We show how to recognize these graphs in polynomial time. We also introduce a new class of blossom-type inequalities that tighten the general linear programming relaxation. A complete description of the convex hull of 1-restricted simple 2-matchings is unknown.