A Simple Proof for Folds on Both Sides in Complexes of Graph Homomorphisms
نویسنده
چکیده
In this paper we study implications of folds in both parameters of Lovász’ Hom(−,−) complexes. There is an important connection between the topological properties of these complexes and lower bounds for chromatic numbers. We give a very short and conceptual proof of the fact that if G− v is a fold of G, then bdHom(G,H) collapses onto bdHom(G − v,H), whereas Hom(H,G) collapses onto Hom(H,G− v). We also give an easy inductive proof of the only nonelementary fact which we use for our arguments: if φ is a closure operator on P , then ∆(P ) collapses onto ∆(φ(P )).
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