Bounded dilation maps of hypercubes into Cayley graphs on the symmetric group

Abstract

LetG andH be graphs with ¦V(G)≤ ¦V(H)¦. Iff:V(G) →V(H) is a one-to-one map, we letdilation(f) be the maximum of distH(fx),f(y)) over all edgesxy inG where distH denotes distance inH. The construction of maps fromG toH of small dilation is motivated by the problem of designing small slowdown simulations onH of algorithms that were originally designed for the networkG.