Complexes of Graph Homomorphisms

  title={Complexes of Graph Homomorphisms},
  author={Dmitry N. Kozlov},
Hom (G, H) is a polyhedral complex defined for any two undirected graphs G and H. This construction was introduced by Lovász to give lower bounds for chromatic numbers of graphs. In this paper we initiate the study of the topological properties of this class of complexes. We show that Hom (K2, Kn) is a boundary complex of a polytope, on which the natural Z2-action on the first argument, induces an antipodal action. We prove that Hom (Km, Kn) is homotopy equivalent to a wedge of (n − m… CONTINUE READING

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