We study the concurrence of arbitrary dimensional multipartite quantum systems. An explicit analytical lower bound of concurrence for four-partite mixed states is obtained in terms of the concurrences of tripartite mixed states. Detailed examples are given to show that our lower bounds improve the existing lower bounds of concurrence. The approach is generalized to five-partite quantum systems.

In this paper, we construct a measure of entanglement by generalizing the quadric polynomial of the Segre variety for general multipartite states. We give explicit expressions for general pure three-partite and four-partite states. Moreover, we will discuss and compare this measure of entanglement with the generalized concurrence.

A digraph obtained by replacing each edge of a complete m-partite graph by an arc or a pair of mutually opposite arcs with the same end vertices is called a semicomplete m-partite digraph. We describe results (theorems and algorithms) on directed walks in semicomplete mpartite digraphs including some recent results concerning tournaments.

Abstract Generalizing well‐known results of Erdős and Lovász, we show that every graph contains a spanning ‐partite subgraph with , where is the edge‐connectivity . In particular, together result due to Nash‐Williams Tutte, this implies 7‐edge‐connected bipartite whose edge set decomposes into two edge‐disjoint trees. We best possible as it does not hold for infinitely many 6‐edge‐connected gra...

It is known that every hypercube Qn is a bipartite graph. Assume that n 2 and F is a subset of edges with |F | n− 2. We prove that there exists a hamiltonian path in Qn − F between any two vertices of different partite sets. Moreover, there exists a path of length 2n − 2 between any two vertices of the same partite set. Assume that n 3 and F is a subset of edges with |F | n− 3. We prove that th...

A digraph obtained by replacing each edge of a complete n-partite (n 2:: 2) graph by an arc or a pair of mutually opposite arcs with the same end vertices is called a semicomplete n-partite digraph or semicomplete multipartite digraph (abbreviated to SMD). In this paper we show the following result for a semicomplete multipartite digraph of order p with the partite sets VI, 112, ... , Vn. Let r...

Using the modified tensor product of graphs defined in [1], we present here a graphical criterion for the separability of m-partite pure quantum states living in a real or complex Hilbert space. The criterion gives both necessary and sufficient condition for the separability of such states. This criterion was first conjectured by S. L. Braunstein, S. Ghosh, T. Mansour, S. Severini, and R. C. Wi...

The complete multipartite graph with d partite sets, each containing m vertices, will be denoted by K(d; m). If all of the partite sets are not of the same cardinality, the graph K(mi, m2, . . . . md) is the complete d-partite graph with m, vertices in each partite sets, 1 <i<d. The special case where mi= 1 for every i, yields the complete graph on d vertices and is denoted by Kd. The join of g...

In this note, we show how optimal or approximate weighted independent sets in k-partite graphs may yield to a good approximate weighted independent set in general graphs. Precisely, optimal solutions in bipartite graphs do yield to a 2 ∆(G) approximation and, more generally, ρ-approximate solutions in k-partite graphs yield to a k ∆(G)ρ-approximation in general graphs.