TTMS19. Embedding Euclidean Distance Graphs in Q^n , in R^n , and then, Back Again
Speaker: Matt Noble, Middle Georgia State University
Abstract: For S subset R, positive integer n, and positive number d, let G(Sn, d) be the graph whose vertex set is Sn where any two vertices are adjacent if and only if they are Euclidean distance d apart. The primary question we will consider is as follows. Given n and distance d actually realized as a distance between points of the rational space Qn, does there exist a graph G that appears as a subgraph of G(Qn, d) but not as a subgraph of G(R(n-1), 1)? In this talk, we will answer this question affirmatively for n less than or equal 5, and along the way, perhaps rustle up a few related questions as well.