Cover-preserving embeddings of bipartite orders into Boolean lattices

Abstract

We study the question which bipartite ordered sets are order-preserving embeddable into two consecutive levels of a Boolean lattice. This is related to investigations on parallel computer architectures, where bipartite networks are embedded into hypercube networks. In our main Theorem we characterize these orders by the existence of a suited edge-coloring of the covering graph. We analyze the representations of cycle-free orders, crowns and glued crowns and present an infinite family of orders which are not embeddable. Their construction shows that this embeddability is not characterizable by a finite number of forbidden suborders.