We consider hypergraphs with unordered hyperedges of unbounded rank. Each hypergraph has a unique modular decomposition, which is a tree, the nodes of which consist of certain prime subhypergraphs of the considered hypergraph. One can define this decomposition by Monadic Second-order (MS) logical formulas. Such a hypergraph is convex if the vertices are linearly ordered in such a way that the h...

Adaptive scientific computations require that periodic repartitioning (load balancing) occur dynamically to maintain load balance. Hypergraph partitioning is a successful model for minimizing communication volume in scientific computations, and partitioning software for the static case is widely available. In this paper, we present a new hypergraph model for the dynamic case, where we minimize ...

In this paper, we show that the eigenvectors of the zero Laplacian and signless Lapacian eigenvalues of a k-uniform hypergraph are closely related to some configured components of that hypergraph. We show that the components of an eigenvector of the zero Laplacian or signless Lapacian eigenvalue have the same modulus. Moreover, under a canonical regularization, the phases of the components of t...

In this paper we present a graph property with sensitivity Θ( √ n), where n = (v 2 ) is the number of variables, and generalize it to a k-uniform hypergraph property with sensitivity Θ( √ n), where n = (v k ) is again the number of variables. This yields the smallest sensitivity yet achieved for a k-uniform hypergraph property. We then show that, for even k, there is a k-uniform hypergraph prop...

The Transversal Hypergraph Generation is the problem of generating, given a hypergraph, the set of its minimal transversals, i.e., the hypergraph whose hyperedges are the minimal hitting sets of the given one. The purpose of this paper is to present an efficient and practical algorithm for solving this problem. We show that the proposed algorithm operates in a way that rules out regeneration an...

Fix integers t ≥ r ≥ 2 and an r-uniform hypergraph F . We prove that the maximum number of edges in a t-partite r-uniform hypergraph on n vertices that contains no copy of F is ct,F ( n r ) + o(nr), where ct,F can be determined by a finite computation. We explicitly define a sequence F1, F2, . . . of r-uniform hypergraphs, and prove that the maximum number of edges in a t-chromatic r-uniform hy...

In this paper we extend the study of bipartite graphs with the induced ε-density property introduced by Frankl, Rödl, and the author. For a given kpartite k-uniform hypergraph G we say that a k-partite k-uniform hypergraph R = (W1, . . . ,Wk,F) has the induced ε-density property if every subhypergraph ofR with at least ε|F| edges contains a copy of G which is an induced subhypergraph of R. We s...

Generated a hypergraph-based network of organic chemistry where hyperedges represent reactions and nodes reactants products. The statistics such hypergraph is reported along with AI applications for predicting reaction class.

An abstract convexity space on a connected hypergraph H with vertex set V (H) is a family C of subsets of V (H) (to be called the convex sets of H) such that: (i) C contains the empty set and V (H), (ii) C is closed under intersection, and (iii) every set in C is connected in H. A convex set X of H is a minimal vertex convex separator of H if there exist two vertices of H that are separated by ...

A string generating hypergraph grammar is a hyperedge replacement grammar where the resulting language consists of string graphs i.e. hypergraphs modeling strings. With the help of these grammars, string languages like anbncn can be modeled that can not be generated by context-free grammars for strings. They are well suited to model discontinuous constituents in natural languages, i.e. constitu...