Abstract
This paper establishes a necessary and sufficient condition for a CO-irredundant set of vertices of a graph to be maximal and shows that the smallest cardinality of a maximal CO-irredundant set in an n vertex graph with maximum degree Δ is bounded below by n / 2 for Δ = 2 , 4 n / 13 for Δ = 3 and 2 n / ( 3 Δ - 3 ) for Δ ⩾ 4 . This result is best possible and extremal graphs are characterised for Δ ⩾ 3 .
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