, Volume 11, Issue 2, pp 199-200
Date: 17 Nov 2012

The stable set problem: some structural properties and relaxations

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This is a summary of the author’s PhD thesis supervised by Antonio Sassano and defended on June 4, 2012 at Sapienza Università di Roma. The thesis is written in English and is available at http://padis.uniroma1.it/bitstream/10805/1598/1/thesisCarlaMichini.pdf. The thesis deals with a polyhedral study of the fractional stable set polytope and aims mainly at establishing some new structural properties of this polytope.

The fractional stable set polytope is the polytope defined by the linear relaxation of the edge formulation of the stable set problem. The edge formulation is defined by two-variable constraints, one for each edge of a graph \(G\), expressing the simple condition that two adjacent nodes cannot belong to a stable set. Even if the fractional stable set polytope is a weak approximation of the stable set polytope, its simple geometrical structure provides deep theoretical insight as well as interesting algorithmic opportunities.

Exploiting a graphic characterization of the bases ...