Kings and serfs in oriented graphs

Abstract

In this paper, we extend the concept of kings and serfs in tournaments to that of weak kings and weak serfs in oriented graphs. We obtain various results on the existence of weak kings(weak serfs) in oriented graphs, and show the existence of n-oriented graphs containing exactly k weak kings(weak serfs). Also, we give the existence of n-oriented graphs containing exactly k weak kings and exactly s weak serfs such that b weak kings from k are also weak serfs.