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

  • David Hartvigsen
  • Yanjun Li
Conference paper

DOI: 10.1007/978-3-540-72792-7_4

Volume 4513 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Hartvigsen D., Li Y. (2007) Triangle-Free Simple 2-Matchings in Subcubic Graphs (Extended Abstract). In: Fischetti M., Williamson D.P. (eds) Integer Programming and Combinatorial Optimization. IPCO 2007. Lecture Notes in Computer Science, vol 4513. Springer, Berlin, Heidelberg

Abstract

A simple 2-matching in 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.

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • David Hartvigsen
    • 1
  • Yanjun Li
    • 2
  1. 1.Mendoza College of Business, University of Notre Dame, Notre Dame, IN 46556USA
  2. 2.Krannert School of Management, Purdue University, West Lafayette, IN 47907USA