Irredundance number versus domination number

AbstractThe domination number γ(G) and the irredundance number ir(G) of a graph G have been considered by many authors from a graph-theoretic or from an algorithmic point of view. In this graph-theoretic paper the infimum of all quotients ir(G)⧸γ(G) is investigated. It is well known that ir(G)⩽γ(G) holds for all undirected graphs G. We show that 23 is the infimum of all quotients ir(T)⧸γ(T) in which T is a tree. Furthermore, there is no tree that attains the infimum. An analogous result for graphs is already known