Decompositions of n-Partite Nonsignaling Correlation-Type Tensors With Applications

Decompositions of moment tensors

Orthogonal Rank Decompositions for Tensors

The theory of orthogonal rank decompositions for matrices is well understood, but the same is not true for tensors. For tensors, even the notions of orthogonality and rank can be interpreted several diierent ways. Tensor decompositions are useful in applications such as principal component analysis for multiway data. We present two types of orthogonal rank decompositions and describe methods to...

Hamilton cycle decompositions of k-uniform k-partite hypergraphs

Let m ≥ 2 and k ≥ 2 be integers. We show that K k×m has a decomposition into Hamilton cycles of Kierstead-Katona type if k | m. We also show that K (3) 3×m − T has a decomposition into Hamilton cycles where T is a 1-factor if and only if 3 m and m = 4. We introduce a notion of symmetry and comment on the existence of symmetric Hamilton cycle decompositions of K (k) k×m.

On n-partite Tournaments with Unique n-cycle

An n-partite tournament is an orientation of a complete n-partite graph. An npartite tournament is a tournament, if it contains exactly one vertex in each partite set. Douglas, Proc. London Math. Soc. 21 (1970) 716-730, obtained a characterization of strongly connected tournaments with exactly one Hamilton cycle (i.e., n-cycle). For n ≥, we characterize strongly connected n-partite tournaments ...

Group magicness of complete n-partite graphs

Let A be a non-trivial Abelian group. We call a graph G = (V, E) A-magic if there exists a labeling f : E → A∗ such that the induced vertex set labeling f : V → A, defined by f(v) = ∑ uv∈E f(uv) is a constant map. In this paper, we show that Kk1,k2,...,kn (ki ≥ 2) is A-magic, for all A where |A| ≥ 3.