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On the dominating set polytope

Bouchakour, Mustapha; Contenza, Teresa; Lee, C.W; Mahjoub, Ali Ridha (2008), On the dominating set polytope, European Journal of Combinatorics, 29, 3, p. 652-661. http://dx.doi.org/10.1016/j.ejc.2007.03.010

Type
Article accepté pour publication ou publié
Date
2008
Journal name
European Journal of Combinatorics
Volume
29
Number
3
Publisher
Elsevier
Pages
652-661
Publication identifier
Metadata
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Author(s)
Bouchakour, Mustapha
Contenza, Teresa
Lee, C.W
Mahjoub, Ali Ridha
Abstract (EN)
In this paper, we study the dominating set polytope in the class of graphs that decompose by one-node cutsets where the pieces are cycles. We describe some classes of facets and procedures to construct facets of the polytope in that class of graphs, and establish some structural properties. As a consequence we obtain a complete description of the polytope by a system of inequalities when the graph is a cycle. We also show that the separation problem related to that system can be solved in polynomial time. This yields a polynomial time cutting plane algorithm for the minimum weight dominating set problem in that case. We further discuss the applications for the class of cactus graphs.
Subjects / Keywords
Polytope