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    Rank-Perfect and Weakly Rank-Perfect Graphs (2001)
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    Publication Date: 2014-11-10
    Description: An edge of a perfect graph $G$ is critical if $G-e$ is imperfect. We would like to decide whether $G - e$ is still {\sl almost perfect} or already {\sl very imperfect}. Via relaxations of the stable set polytope of a graph, we define 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.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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