In this paper, we study coarse embeddings of graphs into Hilbert space. For a graph &Gamma expressible as an infinite union of coarsely embeddable subgraphs, &Gammai, we prove that if the nerve of the covering of &Gamma by the &Gammai is a tree and any nonempty intersections of the subgraphs have universally bounded diameter then &Gamma is coarsely embeddable into a Hilbert space.
Bacon, Dylan and Perlman, Michael
"Coarse embeddings of graphs into Hilbert space,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 16:
2, Article 10.
Available at: https://scholar.rose-hulman.edu/rhumj/vol16/iss2/10