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Polyhedron of triangle-free simple 2-matchings in subcubic graphs

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Abstract

A simple 2-matching in an edge-weighted graph is a subgraph all of whose nodes have degree 0, 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 traveling salesman problem (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.

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Authors and Affiliations

  1. Mendoza College of Business, University of Notre Dame, Notre Dame, IN, 46556, USA

    David Hartvigsen

  2. Krannert School of Management, Purdue University, West Lafayette, IN, 47907, USA

    Yanjun Li

Authors
  1. David Hartvigsen
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  2. Yanjun Li
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Correspondence to David Hartvigsen.

Additional information

An extended abstract of this paper [“Triangle-free simple 2-matchings in subcubic graphs (extended abstract)”] appeared in Integer Programming and Combinatorial Optimization, 12th International IPCO Conference, Ithaca, NY, June 2007, Eds.: M. Fischetti and D.P. Williamson, Springer Verlag, Lecture Notes in Computer Science 4513, Berlin (2007) 43–52.

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Hartvigsen, D., Li, Y. Polyhedron of triangle-free simple 2-matchings in subcubic graphs. Math. Program. 138, 43–82 (2013). https://doi.org/10.1007/s10107-012-0516-0

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