Embeddings of complete binary trees into grids and extended grids with total vertex-congestion 1 Original Research Article

Let G and H be two simple, undirected graphs. An embedding of the graph G into the graph H is an injective mapping f from the vertices of G to the vertices of H, together with a mapping which assigns to each edge [u,v] of G a path between f(u) and f(v) in H. The grid M(r,s) is the graph whose vertex set is the set of pairs on nonnegative integers, {(i,j): 0⩽i