Let K=(V,E) be a finite, simple, complete graph. Let d be a positive integer. Let ϕ:E→Rd be a map from the edge set to Euclidean space, such that the preimage of any point in the range defines a connected graph on the entire vertex set V, and the points assigned to the edges of any triangle in K are collinear. Show that the range of ϕ is contained in a line. graph theorycombinatoricsMiklos Schweitzercontests