Triangle-Free Simple 2-Matchings in Subcubic Graphs (Extended Abstract)

Authors:
David Hartvigsen;Yanjun Li
Affiliations:
Mendoza College of Business, University of Notre Dame, Notre Dame, IN 46556, USA;Krannert School of Management, Purdue University, West Lafayette, IN 47907, USA
Venue:
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Year:
2007

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Abstract

A simple 2-matchingin an edge-weighted graph is a subgraph all of whose vertices have degree 1 or 2. We consider the problem of finding a maximum weight simple 2-matching that contains no triangles, which is closely related to a class of relaxations of the TSP. Our main results are, for graphs with maximum degree 3, a complete description of the convex hull of incidence vectors of triangle-free simple 2-matchings and a strongly polynomial time algorithm for the above problem. Our system requires the use of a type of comb inequality (introduced by Grötschel and Padberg for the TSP polytope) that has {0,1,2}-coefficients and hence is more general than the well-known blossom inequality used in Edmonds' characterization of the simple 2-matching polytope.