@misc{Wagler2001, author = {Wagler, Annegret}, title = {Rank-Perfect and Weakly Rank-Perfect Graphs}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6448}, number = {01-18}, year = {2001}, abstract = {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.}, language = {en} }