WEAK COVERING RELATIONS

This paper proposes and justifies a natural way to weaken the concept of covering relation defined on a finite tournament. Various weak cove ring relations, called k-covering relations, are introduced. To each k -covering relation corresponds a strong uncovered set containing all n on k-covered outcomes. It is proved that those strong uncovered sets m ay be empty. Moreover, the set of all tournaments having an empty stro ng uncovered set is characterized within two rather large classes of t ournaments. Finally, we offer a complete study of the cases where the directed graph defined by a k-covering relation coincides with the ini tial tournament.