We introduce the concept of NIC-planar graphs and present the full characterization of NIC-planar complete k-partite graphs.

The preparation of multipartite entangled states is the prerequisite for exploring quantum information networks and quantum computation. In this Letter, we present what we believe is the first experimental demonstration of an eight-partite spatially separated continuous variable (CV) cluster state of optical modes. Via the linearly optical transformation of eight squeezed states of light, the e...

Galeana-Sanchez, H., On the existence of kernels and h-kernels in directed graphs, Discrete Mathematics 110 (1992) 2.51-255. A directed graph D with vertex set V is called cyclically h-partite (h > 2) provided one can partition V = V, + V, +. . + V,_, so that if (u, u) is an arc of D then u E V,, and u E v+, (notation mod h). In this communication we obtain a characterization of cyclically h-pa...

We propose a minimal entanglement generating set for a general multipartite state based on concurrences classes. In particular, we construct concurrence for general three-partite states based on a redefinition of our concurrence classes. This shows that a measure of entanglement for threepartite states can be decomposed into two different classes that are constructed by two different local oper...

Let m ≥ 2 be an integer. We say that a poset P = (X, ) is m-partite if X has a partition X = X1 ∪ · · · ∪Xm such that (1) each Xi forms an antichain in P, and (2) x ≺ y implies x ∈ Xi and y ∈ Xj where i, j ∈ {1, . . . , m} and i < j. If P is m-partite for some m ≥ 2, then we say it is multipartite. – In this article we discuss the order dimension of multipartite posets in general and derive tig...