Independence and upper irredundance in claw-free graphs

It is known that the independence number of a connected claw-free graph <f>G</f> of order <f>n</f> is at most <f>(n+1)/2</f>. We improve this result by showing that this bound still holds for the upper irredundance number <f>IR(G)</f>. We characterize the connected claw-free graphs for which <f>IR(G)=(n+1)/2</f> and give some properties of those graphs for which <f>IR(G)=n/2</f> if <f>n</f> is even or <f>IR(G)=(n−1)/2</f> if <f>n</f> is odd. [Copyright &y& Elsevier]