New graph decompositions with applications to emulations

In this paper we present a new type of graph decomposition called a cut-cover that combines the notions of graph separators and t-neighborhood covers. We show that graphs with good cut-covers can be emulated in hypercubes and we show that planar and certain minor-excluded graphs have good cut-covers. In particular, we show how to emulate any N-node bounded degree planar graph or any N-node bounded degree graph that excludes Klog0(1)N as a minor with constant slowdown on hypercube networks.