Rank-perfect and" weakly rank-perfect graphs

Annegret K. Wagler

Mathematical Methods of Operations Research, 2002, vol. 56, issue 1, 127-149

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 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. Copyright Springer-Verlag Berlin Heidelberg 2002

Keywords: Key words: perfect graph; critical edge; stable set polytope (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:mathme:v:56:y:2002:i:1:p:127-149

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DOI: 10.1007/s001860200203

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