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...

Recent developments in approximate counting have made startling progress developing fast algorithmic methods for approximating the number of solutions to constraint satisfaction problems (CSPs) with large arities, using connections Lovász Local Lemma. Nevertheless, boundaries these CSPs non-Boolean domain are not well-understood. Our goal this article is fill gap and obtain strong inapproximabi...