TY - GEN A1 - Wagler, Annegret T1 - The Classes of Critically and Anticritically Perfect Graphs N2 - We focus on two new types of extremal graphs with respect to perfectness: critically and anticritically perfect graphs that lose their perfectness by simply deleting and adding an arbitrary edge, respectively. We present examples and study properties in order to compare critically and anticritically perfect graphs with minimally imperfect graphs, another type of extremal graphs with respect to perfectness. We discuss two attempts to characterize the classes of all critically and anticritically perfect graphs and give a brief overview on classes of perfect graphs which contain critically or anticritically perfect graphs. T3 - ZIB-Report - 00-29 KW - perfect graphs KW - critically perfect graphs KW - anticritically perfect graphs Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5975 ER -