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  <doc>
    <id>924</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
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    <completedDate>2006-06-01</completedDate>
    <publishedDate>2006-06-01</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The extreme points of QSTAB(G) and its implications</title>
    <abstract language="eng">Perfect graphs constitute a well-studied graph class with a rich structure, reflected by many characterizations w.r.t different concepts. Perfect graphs are, e.g., characterized as precisely those graphs $G$ where the stable set polytope STAB$(G)$ coincides with the clique constraint stable set polytope QSTAB$(G)$. For all imperfect graphs STAB$(G) \subset$ QSTAB$(G)$ holds and, therefore, it is natural to measure imperfection in terms of the difference between STAB$(G)$ and QSTAB$(G)$. Several concepts have been developed in this direction, for instance the dilation ratio of STAB$(G)$ and QSTAB$(G)$ which is equivalent to the imperfection ratio imp$(G)$ of $G$. To determine imp$(G)$, both knowledge on the facets of STAB$(G)$ and the extreme points of QSTAB$(G)$ is required. The anti-blocking theory of polyhedra yields all {\em dominating} extreme points of QSTAB$(G)$, provided a complete description of the facets of STAB$(\overline G)$ is known. As this is typically not the case, we extend the result on anti-blocking polyhedra to a {\em complete} characterization of the extreme points of QSTAB$(G)$ by establishing a 1-1 correspondence to the facet-defining subgraphs of $\overline G$. We discuss several consequences, in particular, we give alternative proofs of several famous results.</abstract>
    <identifier type="serial">06-30</identifier>
    <identifier type="opus3-id">924</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-9249</identifier>
    <enrichment key="SourceTitle">An extended abstract appeared under the title "On Determining the Imperfection Ratio" in: Electronic Notes in Discrete Mathematics 25 (2006) 177-181</enrichment>
    <author>Arie M.C.A. Koster</author>
    <author>Annegret Wagler</author>
    <series>
      <title>ZIB-Report</title>
      <number>06-30</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>perfect graphs</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>imperfection ratio</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>stable set polytope</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="05C17">Perfect graphs</collection>
    <collection role="msc" number="90C57">Polyhedral combinatorics, branch-and-bound, branch-and-cut</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="projects" number="StableSets">StableSets</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/924/ZR-06-30.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/924/ZR-06-30.ps</file>
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