RNA secondary structure prediction is a fundamental problem in structural bioinformatics. The prediction problem is difficult because RNA secondary structures may contain pseudoknots formed by crossing base pairs. We introduce k-partite secondary structures as a simple classification of RNA secondary structures with pseudoknots. An RNA secondary structure is k-partite if it is the union of k ps...

A cycle in a multipartite graph G is gregarious if it contains at most one vertex from each partite set of G. The complete n-partite graph with partite sets of size m, denoted by Kn(m) is shown to have a decomposition into gregarious 4-cycles. The notion of a gregarious 4-cycle decomposition of this type was introduced in [3]. A 4-cycle decomposition of Kn(m) is circular if it is it is invarian...

We study generalization properties of ranking algorithms in the setting of the k-partite ranking problem. In the k-partite ranking problem, one is given examples of instances labeled with one of k ordered ‘ratings’, and the goal is to learn from these examples a real-valued ranking function that ranks instances in accordance with their ratings. This form of ranking problem arises naturally in a...

An $r$-uniform hypergraph is linear if every two edges intersect in at most one vertex. Given a family of hypergraphs $\mathcal{F}$, the Turán number ex$_r^{lin}(n,\mathcal{F})$ maximum on $n$ vertices that does not contain any member $\mathcal{F}$ as subgraph.
 Let $K_l$ be complete graph with $l$ and $r\geq 2$. The $r$-expansion $r$-graph $K_l^+$ obtained from by enlarging each edge $r-2...

In 4] it is conjectured that all diregular c-partite tournaments, with c 4, are pan-cyclic. In this paper we show that all diregular c-partite tournaments, with c 5, are in fact vertex-pancyclic.

A theorem of Lovv asz asserts that (H)== (H) r=2 for every r-partite hy-pergraph H (where and denote the covering number and fractional covering number respectively). Here it is shown that the same upper bound is valid for a more general class of hypergraphs: those which admit a partition (V 1 ; : : : ; V k) of the vertex set and a partition p 1 + +p k of r such that je\V i j p i r=2 for every ...

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.

The problem of finding necessary and sufficient conditions to decompose a complete tripartite graph K(r, s, t) into 5-cycles was first considered by Mahmoodian and Mirzakhani (1995). They stated some necessary conditions and conjectured that these conditions are also sufficient. Since then, many cases of the problem have been solved by various authors; however the case when the partite sets r ≤...