Chordal graphs and upper irredundance, upper domination and independence

Abstract

In this paper we consider the following parameters: IR( G), the upper irredundance number, which is the order of the largest maximal irredundant set, Γ( G), the upper domination number, which is the order of the largest minimal dominating set and β( G), the independence number, which is the order of the largest maximal independent set. It is well known that for any graph G, β(G) ⩽ Γ(G) ⩽ IR(G) . In this paper we show that these parameters are equal for all chordal graphs, and a class of graphs not containing a set of forbidden subgraphs.