Geodesic
Box complexes and homotopy theory of graphs
Homology, homotopy, and applications, Tome 19 (2017) no. 2, pp. 175-197.

Voir la notice de l'article provenant de la source International Press of Boston

We introduce a model structure on the category of graphs, which is Quillen equivalent to the category of $\mathbb{Z}_2$-spaces. A weak equivalence is a graph homomorphism which induces a $\mathbb{Z}_2$-homotopy equivalence between their box complexes. The box complex is a $\mathbb{Z}_2$-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.
DOI : 10.4310/HHA.2017.v19.n2.a10
Classification : 55U10, 05C15
Keywords: graph, neighborhood complex, box complex, Hom complex, model category 
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Takahiro Matsushita. Box complexes and homotopy theory of graphs. Homology, homotopy, and applications, Tome 19 (2017) no. 2, pp. 175-197. doi : 10.4310/HHA.2017.v19.n2.a10. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2017.v19.n2.a10/

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