Gear Composition of Stable Set Polytopes and G-Perfection

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 graph obt...

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Bibliographic Details
Published in:Mathematics of operations research Vol. 34; no. 4; pp. 813 - 836
Main Authors: Galluccio, Anna, Gentile, Claudio, Ventura, Paolo
Format: Journal Article
Language:English
Published: Linthicum Institute for Operations Research and the Management Sciences 01.11.2009
Subjects:
Analysis
Coefficients
Fuzzy sets
Line graphs
Linear inequalities
Linear programming
Linear systems
Mathematical inequalities
Mathematical theorems
Mathematical vectors
Operations research
Polyhedrons
Polytopes
Set theory
Studies
United States
ISSN:0364-765X, 1526-5471
Online Access:Get full text
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Summary: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 graph obtained from H by subdividing the edge e . We also introduce the class of -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 -perfect, provided that any graph obtained from H by subdividing a subset of its simplicial edges is -perfect. In particular, we show that a large subclass of claw-free graphs is -perfect.
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ISSN:0364-765X
1526-5471
DOI:10.1287/moor.1090.0407