Box complexes and homotopy theory of graphs
Takahiro Matsushita · Homology Homotopy and Applications · 2017
We introduce a model structure on the category of graphs, which is Quillen equivalent to the category of Z 2 -spaces.A weak equivalence is a graph homomorphism which induces a Z 2homotopy equivalence between their box complexes.The box complex is a Z 2 -space associated to a graph, considered in the context of the graph coloring problem.In the proof, we discuss the universality problem of the Hom complex.