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Formulations for the Stable Set Polytope
"... We give a simple algorithm for the weighted stable set problem of an arbitrary graph which yields an extended formulation for its stable set polytope The algorithm runs in polynomial time for the class of distance clawfree graphs These are the graphs such that for each node neither its neighbo ..."
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Cited by 8 (1 self)
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We give a simple algorithm for the weighted stable set problem of an arbitrary graph which yields an extended formulation for its stable set polytope The algorithm runs in polynomial time for the class of distance clawfree graphs These are the graphs such that for each node neither its
Critical Facets of the Stable Set Polytope
"... A facet of the stable set polytope of a graph G can be viewed as a generalization of the notion of an #critical graph. We extend several results from the theory of #critical graphs to facets. The defect of a nontrivial, fulldimensional facet # v#V a(v)x v # b of the stable set polytope of a g ..."
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Cited by 8 (1 self)
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A facet of the stable set polytope of a graph G can be viewed as a generalization of the notion of an #critical graph. We extend several results from the theory of #critical graphs to facets. The defect of a nontrivial, fulldimensional facet # v#V a(v)x v # b of the stable set polytope of a
Wheel Inequalities for Stable Set Polytopes
, 1996
"... We introduce new classes of valid inequalities, called wheel inequalities, for the stable set polytope PG of a graph G. Each "wheel configuration" gives rise to two such inequalities. The simplest wheel configuration is an "odd" subdivision W of a wheel, and for these we give ne ..."
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Cited by 12 (0 self)
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We introduce new classes of valid inequalities, called wheel inequalities, for the stable set polytope PG of a graph G. Each "wheel configuration" gives rise to two such inequalities. The simplest wheel configuration is an "odd" subdivision W of a wheel, and for these we give
The Hirsch Conjecture for the Fractional Stable Set Polytope
, 2012
"... The edge formulation of the stable set problem is defined by twovariable constraints, one for each edge of a graph G, expressing the simple condition that two adjacent nodes cannot belong to a stable set. We study the fractional stable set polytope, i.e. the polytope defined by the linear relaxatio ..."
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Cited by 1 (0 self)
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The edge formulation of the stable set problem is defined by twovariable constraints, one for each edge of a graph G, expressing the simple condition that two adjacent nodes cannot belong to a stable set. We study the fractional stable set polytope, i.e. the polytope defined by the linear
Stable Set Polytopes for a Class of Circulant Graphs
 SIAM J. OPTIM
, 1997
"... We study the stable set polytope P (Gn ) for the graph Gn with n nodes and edges [i, j] when ij # 2 (using modulo n calculation); this graph coincides with the antiweb W (n, 3). A minimal linear system defining P (Gn ) is determined. The system consists of certain rank inequalities with some ..."
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Cited by 7 (1 self)
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We study the stable set polytope P (Gn ) for the graph Gn with n nodes and edges [i, j] when ij # 2 (using modulo n calculation); this graph coincides with the antiweb W (n, 3). A minimal linear system defining P (Gn ) is determined. The system consists of certain rank inequalities with some
The Stable Set Polytope of QuasiLine Graphs
"... It is a long standing open problem to find an explicit description of the stable set polytope of clawfree graphs. Yet more than 20 years after the discovery of a polynomial algorithm for the maximum stable set problem for clawfree graphs, there is even no conjecture at hand today. Such a conjectur ..."
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Cited by 10 (5 self)
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It is a long standing open problem to find an explicit description of the stable set polytope of clawfree graphs. Yet more than 20 years after the discovery of a polynomial algorithm for the maximum stable set problem for clawfree graphs, there is even no conjecture at hand today. Such a
Facets With Fixed Defect of the Stable Set Polytope
, 1999
"... The stable set polytope of a graph is the convex hull of the 01 vectors corresponding to stable sets of vertices. To any nontrivial facet # n i=1 a i x i # b of this polytope we associate an integer #, called the defect of the facet, by # = # n i=1 a i  2b. We show that for any fixed # ther ..."
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Cited by 5 (2 self)
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The stable set polytope of a graph is the convex hull of the 01 vectors corresponding to stable sets of vertices. To any nontrivial facet # n i=1 a i x i # b of this polytope we associate an integer #, called the defect of the facet, by # = # n i=1 a i  2b. We show that for any fixed
On NonRank Facets of Stable Set Polytopes of Webs with Clique Number Four
, 2005
"... Graphs with circular symmetry, called webs, are relevant for describing the stable set polytopes of two larger graph classes, quasiline graphs [6,10] and clawfree graphs [5,6]. Providing a decent linear description of the stable set polytopes of clawfree graphs is a longstanding problem [7]. Howe ..."
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Cited by 3 (3 self)
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Graphs with circular symmetry, called webs, are relevant for describing the stable set polytopes of two larger graph classes, quasiline graphs [6,10] and clawfree graphs [5,6]. Providing a decent linear description of the stable set polytopes of clawfree graphs is a longstanding problem [7
NEW FACET DEFINING INEQUALITIES FOR THE STABLE SET POLYTOPE
, 2006
"... We present a new graph composition that produces a graph G from a given graph H and a fixed graph B called gear and we study its polyhedral properties. This composition yields counterexamples to a conjecture on the facial structure of STAB(G) when G is clawfree. ..."
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We present a new graph composition that produces a graph G from a given graph H and a fixed graph B called gear and we study its polyhedral properties. This composition yields counterexamples to a conjecture on the facial structure of STAB(G) when G is clawfree.
About Facets of the Stable Set Polytope of a Graph
, 2000
"... No complete characterization of rank facet producing graphs is known. In 1977, Balas and Zemel gave a necessary for a graph to be rankfacet producing, and in 1975, Chvtal gave a sufficient condition, which motivated the study of the class of αcritical graphs. We give two strengthening of ..."
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No complete characterization of rank facet producing graphs is known. In 1977, Balas and Zemel gave a necessary for a graph to be rankfacet producing, and in 1975, Chvtal gave a sufficient condition, which motivated the study of the class of αcritical graphs. We give two strengthening of Balas and Zemel's necessary condition, and one of Chvatal's sufficient condition.
Results 1  10
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1,341,597