Two relations between the parameters of independence and irredundance

Abstract In a simple graph, n, δ, i and IR denote respectively the number of vertices, the minimum degree, the order of a minimum maximal independent set and the order of a maximum irredundant set. We show that i + IR⩽2n + 2δ − 2 2nδ , which was conjectured by Cockayne, Favaron, Payan and Thomason, and that i + 2 δIR ⩽n + δ .