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  Rank-Perfect and Weakly Rank-Perfect Graphs [1 citations — 0 self]

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by Annegret K. Wagler, Annegret K. Wagler
Mathematical Methods of Operations Research
ftp://ftp.zib.de/pub/zib-publications/reports/ZR-01-18.ps
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Abstract:

An edge e of a perfect graph G is critical if G e is imperfect. We would like to decide whether G e is still \almost perfect " or already \very imperfect". Via relaxations of the stable set polytope of a graph, we dene two superclasses of perfect graphs: rank-perfect and weakly rank-perfect graphs. Membership in those two classes indicates how far an imperfect graph is away from being perfect. We study the cases, when a critical edge is removed from the line graph of a bipartite graph or from the complement of such a graph. 1

Citations

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