Title:  The complex of not 2-connected graphs

Abstract:  With every graph property that is monotone, we can associate for every positive integer n an abstract simplicial complex. The vertices of this complex are the edges of the complete graph on n nodes, and the faces are the sets of edges having this graph property. We will present and outline the proof of a result by Babson, Bjorner, Linusson, Shareshian and Welker of the homotopy type of this simplicial complex for not 2-connected graphs.