The stable set polytope of claw-free graphs with stability number at least four. II. Striped graphs are<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="script">G</mml:mi></mml:math>-perfect

Galluccio, Anna; Gentile, Claudio; Ventura, Paolo

doi:10.1016/j.jctb.2014.02.009

Cited by 7 publications

(3 citation statements)

References 12 publications

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“…In [20,21] we proved that all graphs in Z * and their contraction along simplicial edges satisfying (**) are G-perfect. This result together with Theorem 12 and Theorem 14 yields the following:…”

Section: Theorem 12mentioning

confidence: 99%

2-clique-bond of stable set polyhedra

Galluccio

Gentile

Ventura

2013

Discrete Applied Mathematics

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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 G 1 and G 2 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 G 1 and G 2 .We show how to apply the 2-clique-bond composition to provide the complete linear description of large classes of graphs.

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Section: Theorem 12mentioning

confidence: 99%

2-clique-bond of stable set polyhedra

Galluccio

Gentile

Ventura

2013

Discrete Applied Mathematics

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“…The problem of characterizing STAB(G) when G is a connected claw-free but not quasi-line graph with α(G) ≥ 4 was studied by Galluccio et al: In a series of results [13,14,15], it is shown that if such a graph G does not contain a clique cutset, then 1,2-valued constraints suffice to describe STAB(G). Here, besides 5-wheels, different rank and non-rank facet-defining inequalities of the geared graph G shown in Fig.…”

Section: About Claw-free Graphsmentioning

confidence: 99%

“…For that, it surprisingly turned out that it was not necessary to make use of the description of STAB(G) for claw-free not quasi-line graphs G -with α(G) = 2 (by Cook, see [31]), -with α(G) = 3 (by Pêcher, Wagler [28]), -with α(G) ≥ 4 (by Galluccio, Gentile, Ventura [13,14,15]). …”

Section: Conclusion and Future Researchmentioning

confidence: 99%

Lovász-Schrijver PSD-Operator on Claw-Free Graphs

Bianchi

Escalante

Nasini

et al. 2016

Lecture Notes in Computer Science

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Abstract. The subject of this work is the study of LS+-perfect graphs defined as those graphs G for which the stable set polytope STAB(G) is achieved in one iteration of Lovász-Schrijver PSD-operator LS+, applied to its edge relaxation ESTAB(G). In particular, we look for a polyhedral relaxation of STAB(G) that coincides with LS+(ESTAB(G)) and STAB(G) if and only if G is LS+-perfect. An according conjecture has been recently formulated (LS+-Perfect Graph Conjecture); here we verify it for the well-studied class of claw-free graphs.

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