We investigate asymptotic distillation of entanglement in the presence of an unlimited amount of bound entanglement for bi-partite systems. We show that the distillability is still bounded by the relative entropy of entanglement. This offers a strong support to the fact that bound entanglement does not improve distillation of entanglement. PACS number(s): 03.65.Bz, 89.70.+c,89.80.+h keywords: e...

In this paper, we study the problem of efficiently mining frequent partite episodes that satisfy partwise constraints from an input event sequence. Through our constraints, we can extract episodes related to events and their precedent-subsequent relations, on which we focus, in a short time. This improves the efficiency of data mining using trial and error processes. A partite episode of length...

Generally, a graph G, an independent set is a subset S of vertices in G such that no two vertices in S are adjacent (connected by an edge) and a vertex cover is a subset S of vertices such that each edge of G has at least one of its endpoints in S. Again, the minimum vertex cover problem is to find a vertex cover with the smallest number of vertices. Consider a k-partite graph G = (V, E) with v...

A semicomplete multipartite or semicomplete c-partite digraph D is a biorientation of a c-partite graph. A semicomplete multipartite digraph D is called strongly quasiHamiltonian-connected, if for any two distinct vertices x and y of D, there is a path P from x to y such that P contains at least one vertex from each partite set of D. In this paper we show that every 4-strong semicomplete multip...

We call a 2-partite digraph D homogeneous if every isomorphism between finite induced subdigraphs that respects the 2-partition of D extends to an automorphism of D that does the same. In this note, we classify the homogeneous 2-partite digraphs.

We show that in any n-partite tournament, where n/> 3, with no transmitters and no 3-kings, the number of 4-kings is at least eight. All n-partite tournaments, where n/>3, having eight 4-kings and no 3-kings are completely characterized. This solves the problem proposed in Koh and Tan (accepted).

In this paper we prove that if T is a regular n-partite tournament with n ≥ 4, then each arc of T lies on a cycle whose vertices are from exactly k partite sets for k = 4, 5, . . . , n. Our result, in a sense, generalizes a theorem due to Alspach.