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.

Author Bio

Dylan Bacon is an Applied Mathematics and Computer Science major at the University of Wisconsin - Stout. After graduation he hopes to enter a job in industry as a database administrator or to enter research for relational data, combining mathematics and computer science.Faculty Sponsor: Matthew Horak, Department of Mathematics, Statistics, and Computer Science, University of Wisconsin-Stout

Michael Perlman is a recent graduate in Mathematics from the University of Illinois at Chicago. He entered the Mathematics Ph.D. program at the University of Notre Dame in the fall of 2015. Michael's research interests include commutative algebra and algebraic geometry.