On the complexity of the embedding problem for hypercube related graphs

AbstractThe n-dimensional hypercube is the graph with 2n nodes labelled 0,1,…,2n−1 and an edge joining two nodes whenever their binary representation differs in a single coordinate. The problem of deciding whether a given graph is a subgraph of an n-dimensional cube has recently been shown to be NP-complete. In this paper we illustrate a reduction technique used to obtain NP-completeness results for a variety of hypercube related graphs. We consider the subgraph isomorphism problem on two related families of graphs, the dilation two hypercubes and generalized hypercubes. We show that the embedding problem for both of these families is NP-complete