On the Steiner 2-edge connected subgraph polytope
RAIRO - Operations Research - Recherche Opérationnelle, Tome 42 (2008) no. 3, pp. 259-283.

In this paper, we study the Steiner 2-edge connected subgraph polytope. We introduce a large class of valid inequalities for this polytope called the generalized Steiner F-partition inequalities, that generalizes the so-called Steiner F-partition inequalities. We show that these inequalities together with the trivial and the Steiner cut inequalities completely describe the polytope on a class of graphs that generalizes the wheels. We also describe necessary conditions for these inequalities to be facet defining, and as a consequence, we obtain that the separation problem over the Steiner 2-edge connected subgraph polytope for that class of graphs can be solved in polynomial time. Moreover, we discuss that polytope in the graphs that decompose by 3-edge cutsets. And we show that the generalized Steiner F-partition inequalities together with the trivial and the Steiner cut inequalities suffice to describe the polytope in a class of graphs that generalizes the class of Halin graphs when the terminals have a particular disposition. This generalizes a result of Barahona and Mahjoub [4] for Halin graphs. This also yields a polynomial time cutting plane algorithm for the Steiner 2-edge connected subgraph problem in that class of graphs.

DOI : 10.1051/ro:2008022
Classification : 05C85, 90C27
Mots clés : polytope, Steiner $2$-edge connected graph, Halin graph
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Mahjoub, A. Rhida; Pesneau, Pierre. On the Steiner $2$-edge connected subgraph polytope. RAIRO - Operations Research - Recherche Opérationnelle, Tome 42 (2008) no. 3, pp. 259-283. doi : 10.1051/ro:2008022. http://www.numdam.org/articles/10.1051/ro:2008022/

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