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2-clique-bond of stable set polyhedra

Anna Galluccio (galluccio***at***iasi.cnr.it)
Claudio Gentile (gentile***at***iasi.cnr.it)
Paolo Ventura (ventura***at***iasi.cnr.it)

Abstract: The 2-bond is a generalization of the 2-join where the subsets of nodes that are connected on each shore of the partition are not necessarily disjoint. If all the subsets are cliques we say that the 2-bond is a 2-clique-bond. We consider a graph G obtained as the 2-clique-bond of two graphs G1 and G2 and we study the polyhedral properties of the stable set polytope associated with this graph. In particular, we prove that a linear description of the stable set polytope of G is obtained by properly composing the linear inequalities describing the stable set polytopes of four graphs that are related to G1 and G2. We show how to apply the 2-clique-bond composition to provide the complete linear description of large classes of graphs.

Keywords: Stable set polytope, graph compositions, 2-join, polyhedral combinatorics.

Category 1: Combinatorial Optimization (Polyhedra )

Category 2: Integer Programming (0-1 Programming )

Citation: A preliminary version of this paper appeared as G. Galluccio, C. Gentile, P.Ventura, 2-clique-bond of stable set polyhedra, Tech. Rep. 09-10, IASI-CNR, 2009.

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Entry Submitted: 03/15/2011
Entry Accepted: 03/15/2011
Entry Last Modified: 04/19/2013

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