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

  • Conference paper
Book cover Integer Programming and Combinatorial Optimization (IPCO 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4513))

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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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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Editor information

Matteo Fischetti David P. Williamson

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© 2007 Springer Berlin Heidelberg

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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. https://doi.org/10.1007/978-3-540-72792-7_4

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  • DOI: https://doi.org/10.1007/978-3-540-72792-7_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72791-0

  • Online ISBN: 978-3-540-72792-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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