On a class of kernel-perfect and kernel-perfect-critical graphs

Abstract In this note we present a construction of a class of graphs in which each of the graphs is either kernel-perfect or kernel-perfect-critical. These graphs originate from the theory of games (Von Neumann and Morgenstern). We also find criteria to distinguish kernel-perfect graphs from kernel- perfect-critical graphs in this class. We obtain some of the previously known classes of kernel- perfect-critical graphs as special cases of the present construction given here. The construction that we give enlarges the class of kernel-perfect-critical graphs.