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Restricted 2-factor polytopes

Cunningham, William H. and Wang, Yaoguang

February 1997, 30 pages.

Status: available - back from printing

The optimal $k$-restricted 2-factor problem consists of finding, in a complete undirected graph $K_n$, a minimum cost 2-factor (subgraph having degree 2 at every node) with all components having more than $k$ nodes. The problem is a relaxation of the well-known symmetric travelling salesman problem, and is equivalent to it when $\frac{n}{2}\leq k\leq n-1$. We study the $k$-restricted 2-factor polytope. We present a large class of valid inequalities, called bipartition inequalities, and describe some of their properties; some of these results are new even for the travelling salesman polytope. For the case $k=3$, the triangle-free 2-factor polytope, we derive a necessary and sufficient condition for such inequalities to be facet inducing.

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  AUTHOR = {Cunningham, William H. and Wang, Yaoguang},
  TITLE = {Restricted 2-factor polytopes},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-97-1-006},
  MONTH = {February},
  YEAR = {1997},
  ISSN = {0946-011X},