Box complexes and homotopy theory of graphs

Takahiro Matsushita

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arXiv · 1605.06222

Box complexes and homotopy theory of graphs

Takahiro Matsushita

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Abstract

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.

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BibTeX RIS

Takahiro Matsushita. 2017-07-29. Box complexes and homotopy theory of graphs. https://arxiv.org/abs/1605.06222

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