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Box Complexes and Homotopy Theory of Graphs by Matsushita, Takahiro is a scholarly article available to read on EtoBox.

What is Box Complexes and Homotopy Theory of Graphs about?

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.

Author

Matsushita, Takahiro

Published

2016

Language

EN