NoteOn a lower bound for the connectivity of the independence complex of a graph

Aharoni, Berger and Ziv proposed a function which is a lower bound for the connectivity of the independence complex of a graph. They conjectured that this bound is optimal for every graph. We give two different arguments which show that the conjecture is false.

► The connectivity of the independence complex of a graph is studied. ► We provide an explicit proof of a lower bound proposed by Aharoni, Berger and Ziv. ► The conjecture that this bound is always an equality is disproved. ► Explicit counterexamples to the conjecture are constructed.