Gear Composition of stable set polytopes and G-perfection (Articolo in rivista)

Type
Label
  • Gear Composition of stable set polytopes and G-perfection (Articolo in rivista) (literal)
Anno
  • 2009-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1287/moor.1090.0407 (literal)
Alternative label
  • Galluccio, A.; Gentile, C.; Ventura , P. (2009)
    Gear Composition of stable set polytopes and G-perfection
    in Mathematics of operations research
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Galluccio, A.; Gentile, C.; Ventura , P. (literal)
Pagina inizio
  • 813 (literal)
Pagina fine
  • 836 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 34 (literal)
Rivista
Note
  • ISI Web of Science (WOS) (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • Istituto analisi dei sistemi ed informatica \"Antonio Ruberti\" (literal)
Titolo
  • Gear Composition of stable set polytopes and G-perfection (literal)
Abstract
  • Graphs obtained by applying the gear composition to a given graph H are called geared graphs. We show how a linear description of the stable set polytope STAB(G) of a geared graph G can be obtained by extending the linear inequalities defining STAB(H) and STAB(H^e), where H^e is the the graph obtained from H by subdividing the edge e. We also introduce the class of G-perfect graphs, i.e., graphs whose stable set polytope is described by: nonnegativity inequalities, rank inequalities, lifted 5-wheel inequalities, and some special inequalities called geared inequalities and g-lifted inequalities. We prove that graphs obtained by repeated applications of the gear composition to a given graph H are G-perfect, provided that any graph obtained from H by subdividing a subset of its simplicial edges is G-perfect. In particular, we show that a large subclass of claw-free graphs is G-perfect, thus providing a partial answer to the well-known problem of finding a defining linear system for the stable set polytope of claw-free graphs. (literal)
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