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arXiv · 0712.1269

On the facial structure of Symmetric and Graphical Traveling Salesman Polyhedra

Dirk Oliver Theis
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Abstract

The Symmetric Traveling Salesman Polytope $S_n$ for a fixed number $n$ of cities is a face of the corresponding Graphical Traveling Salesman Polyhedron $P_n$. This has been used to study facets of $S_n$ using $P_n$ as a tool. In this paper, we study the operation of "rotating" (or "lifting") valid inequalities for $S_n$ to obtain a valid inequalities for $P_n$. As an application, we describe a surprising relationship between (a) the parsimonious property of relaxations of the Symmetric Traveling Salesman Polytope and (b) a connectivity property of the ridge graph of the Graphical Traveling Salesman Polyhedron.

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Dirk Oliver Theis. 2009-04-10. On the facial structure of Symmetric and Graphical Traveling Salesman Polyhedra. https://arxiv.org/abs/0712.1269

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