We show that the hypercube has a face-unfolding that tiles space, and that unfolding has an edge-unfolding that tiles the plane. So the hypercube is a “dimension-descending tiler.” We also show that the hypercube cross unfolding made famous by Dali tiles space, but we leave open the question of whether or not it has an edge-unfolding that tiles the plane.

In this paper, we focus on a hypercube-like structure, the folded hypercube, which is basically a standard hypercube with some extra links between its nodes. Let f be a faulty vertex in an n-dimensional folded hypercube FQn. We show that FQn−{f } contains a faultfree cycle of every even length from 4 to 2n−2 if n ≥ 3 and, furthermore, every odd length from n+ 1 to 2n − 1 if n ≥ 2 and n is even....

We present embeddings of generalized ladders as subgraphs into the hypercube. By embedding caterpillars into ladders, we obtain embeddings of caterpillars into the hypercube. In this way we obtain almost all known results concerning the em-beddings of caterpillars into the hypercube. In addition we construct embeddings for some new types of caterpillars.

We derive colour spaces of the hue-colourfulness-luminance type, on the basis of a four-dimensional hypercube I (I = [0, 1]). The hypercube corresponds to a tetrachromatic colour system, analogous to the three-dimensional RGB cube. In the first derived space the colourfulness is chromatic saturation while in the second one, colourfulness refers to the vividness of the colour, even if it is achr...

The hypercube-like networks are a class of important generalization of the popular hypercube interconnection networks for parallel computing. This paper is concerned with the fault-tolerant cycle embedding ability of a subclass of hypercube-like networks, called restricted hypercube-like networks (RHLNs, for short), which include most of the well-known hypercube variants, such as the twisted cu...

The binary hypercube, or n-cube, has been widely used as the interconnection network in parallel computers. However, the major drawback of the hypercube is the increase in the number of communication links for each node with the increase in the total number of nodes in the system. This paper introduces a new interconnection network for large-scale distributed memory multiprocessors called dual-...

Latin hypercube designs have been found very useful for designing computer experiments. In recent years, several methods of constructing orthogonal Latin hypercube designs have been proposed in the literature. In this article, we report some more results on Latin hypercube designs, including several new designs.

We present embeddings of generalized ladders as subgraphs into the hypercube. By embedding caterpillars into ladders, we obtain embeddings of caterpillars into the hypercube. In this way we obtain almost all known results concerning the embeddings of caterpillars into the hypercube. In addition we construct embeddings for some new types of caterpillars.

In this paper, we investigate the validity of the Unique Games Conjecture when the constraint graph is the boolean hypercube. We construct an almost optimal integrality gap instance on the Hypercube for the Goemans-Williamson semidefinite program (SDP) for Max-2-LIN(Z2). We conjecture that adding triangle inequalities to the SDP provides a polynomial time algorithm to solve Unique Games on the ...