On the Simple ℤ2-homotopy Types of Graph Complexes and Their Simple ℤ2-universality

Abstract

AbstractWe prove that the neighborhood complex N(G), the box complex B(G), the homomorphism complex Hom(K2, G) and the Lovász complex L(G) have the same simple ℤ2-homotopy type in the sense of Whitehead. We show that these graph complexes are simple ℤ2-universal.