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#### Restricted 2-factor polytopes

##### MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons45701

Wang,  Yaoguang
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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##### Volltexte (frei zugänglich)

1997-1-006
(beliebiger Volltext), 10KB

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##### Zitation

Cunningham, W. H., & Wang, Y.(1997). Restricted 2-factor polytopes (MPI-I-1997-1-006). Saarbrücken: Max-Planck-Institut für Informatik.

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.