Lovász and Schrijver $$N_+$$ -Relaxation on Web Graphs

Escalante, Mariana S.; Nasini, Graciela L.

doi:10.1007/978-3-319-14115-2_19

Cited by 4 publications

(9 citation statements)

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“…(), fs‐perfect graphs (where the only facet‐defining subgraphs are cliques and the graph itself) by Bianchi et al. (), and webs (the complements of antiwebs) by Escalante and Nasini ().…”

Section: Introductionmentioning

confidence: 99%

Characterizing ‐perfect line graphs

Escalante

Nasini

Wagler

2016

Int Trans Operational Res

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The aim of this paper is to study the Lovász-Schrijver PSD operator N + applied to the edge relaxation of the stable set polytope of a graph. We are particularly interested in the problem of characterizing graphs for which N + generates the stable set polytope in one step, called N + -perfect graphs. It is conjectured that the only N + -perfect graphs are those whose stable set polytope is described by inequalities with near-bipartite support. So far, this conjecture has been proved for near-perfect graphs, fs-perfect graphs, and webs. Here, we verify it for line graphs, by proving that in an N + -perfect line graph the only facet-defining subgraphs are cliques and odd holes.

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Section: Introductionmentioning

confidence: 99%

Characterizing ‐perfect line graphs

Escalante

Nasini

Wagler

2016

Int Trans Operational Res

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“…Based on the results of Eisenbrand et al [9] and Stauffer [33], combined with the characterization of LS + -imperfect webs from [11] (Theorem 4), we are able to show: Theorem 7. All facet-defining LS + -perfect fuzzy circular interval graphs are cliques, odd holes or odd antiholes.…”

Section: Quasi-line Graphsmentioning

confidence: 77%

“…Using stretchings of G LT and G EMN and exhibiting one more minimally LS + -imperfect graph, namely the web W 2 10 , LS + -perfect webs are characterized in [11] as follows:…”

Section: About Ls + -Perfect Graphsmentioning

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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“…Verifying the validity of Conjecture 2 is equivalent to determine the validity of the following two statements: In [6], we made some progress towards proving Conjecture 3, by presenting an infinite family of graphs for which it holds. Recently, Conjecture 4 was verified for web graphs [17]. In this contribution, we prove that Conjecture 4 holds for a class of graphs called fs-perfect graphs that stand for full-support-perfect graphs.…”

Section: Conjecturementioning

confidence: 81%

Lovász–Schrijver SDP-operator, near-perfect graphs and near-bipartite graphs

et al. 2016

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We study the Lovász-Schrijver lift-and-project operator (LS+) based on the cone of symmetric, positive semidefinite matrices, applied to the fractional stable set polytope of graphs. The problem of obtaining a combinatorial characterization of graphs for which the LS+-operator generates the stable set polytope in one step has been open since 1990. We call these graphs LS+-perfect. In the current contribution, we pursue a full combinatorial characterization of LS+perfect graphs and make progress towards such a characterization by establishing a new, close relationship among LS+-perfect graphs, near-bipartite graphs and a newly introduced concept of full-support-perfect graphs.Date: November 6, 2014. Key words and phrases. stable set problem, lift-and-project methods, semidefinite programming, integer programming.Some of the results in this paper were first announced in conference proceedings in abstracts [7,8].

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Lovász and Schrijver $$N_+$$ -Relaxation on Web Graphs

Cited by 4 publications

References 0 publications

Characterizing ‐perfect line graphs

Characterizing ‐perfect line graphs

Lovász-Schrijver PSD-Operator on Claw-Free Graphs

Lovász–Schrijver SDP-operator, near-perfect graphs and near-bipartite graphs

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