Splittings of independence complexes and the powers of cycles

Abstract

We use two cofibre sequences to identify some combinatorial situations when the independence complex of a graph splits into a wedge sum of smaller independence complexes. Our main application is to give a recursive relation for the homotopy types of the independence complexes of powers of cycles, which answers an open question of D. Kozlov.

V4: final version

References in corpus (2)

• Vertex decomposable graphs and obstructions to shellability
• Independence Complexes of Cylinders Constructed from Square and Hexagonal Grid Graphs