Domination and irredundance in tournaments

A set S ⊆ V of vertices in a graph G = (V,E) is called a dominating set if every vertex in V − S is adjacent to at least one vertex in S. Domination in graphs is a well-studied branch of graph theory, and is the subject of two books by Haynes, Hedetniemi and Slater [8, 9]. However, about 90% of the papers on domination have considered only undirected graphs. Thus, relatively little is known about domination and related concepts in directed graphs, and much of what is known is related to the study of kernels in digraphs. For an excellent survey of most of this literature the reader is referred to a chapter on this topic by Ghoshal, Laskar and Pillone [6]. The focus of this paper is the application of the concepts of domination and irredundance in undirected graphs to the study of tournaments. These terms are defined in the next section.