The Rank Facets of the Stable Set Polytope for Claw-Free Graphs

This paper provides a complete characterization of the rank facets of the stable set polytope STAB(G) associated with a claw-free graphG. In particular, it is shown that a claw-free graphGproduces a rank facet of STAB(G) if and only if it can be obtained by means of two simple lifting procedures fro...

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Bibliographic Details
Published inJournal of combinatorial theory. Series B Vol. 69; no. 1; pp. 1 - 38
Main Authors Galluccio, A., Sassano, A.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.01.1997
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Summary:This paper provides a complete characterization of the rank facets of the stable set polytope STAB(G) associated with a claw-free graphG. In particular, it is shown that a claw-free graphGproduces a rank facet of STAB(G) if and only if it can be obtained by means of two simple lifting procedures from three basic classes of graphs: (i) cliques, (ii) line graphs of minimal 2-connected hypomatchable graphs, and (iii) circulant graphsCω−1αω+1. As a by-product, a characterization of the rank facets of STAB(G) having right-hand side 2 is given.
ISSN:0095-8956
1096-0902
DOI:10.1006/jctb.1996.1715