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2007, with author Ventura P., in the category IASI Research Reports
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IASI Research Report n. 661 (Previous Next) Anna Galluccio,

Claudio Gentile,

Paolo VenturaGear composition of stable set polytopes and G-perfectionABSTRACT Graphs obtained by repeated applications of 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: rank inequalities, lifted 5-wheel inequalities and some special inequalities called geared inequalities and g-lifted inequalities. We show that some classes of graphs are G-perfect. In particular, we prove 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.