For a fixed 3-uniform hypergraph F , call a hypergraph F-free if it contains no subhypergraph isomorphic to F . Let ex(n,F) denote the size of a largest F-free hypergraph G ⊆ [n]. Let Fn(F) denote the number of distinct labelled F-free G ⊆ [n]. We show that Fn(F) = 2ex(n,F)+o(n 3), and discuss related problems.

In this paper, we introduce contextual hypergraph grammars, which generalize the total contextual string grammars. We study the position of the class of languages generated by contextual hypergraph grammars in comparison with graph languages generated by hyperedge replacement grammars and double-pushout hypergraph grammars. Moreover, several examples show the potential of the new class of gramm...

This article explores possibilities of partitioning the vertex set of a given simple loop-free Sperner hypergraph into a union of transversals. Studies are done on the possible number of transversals in such partitions, followed by forming a hypergraph (on the vertex set of the given hypergraph) that consists of transversals for hyperedges. AMS Subject Classification: 05C65

Some results on matchings in a hypergraph cut vertex, cut edge of hypergraph have been obtained analogous to the results in a simple graph. In this paper we have obtained some interesting properties of a hypergraph. The notations and terminology that are used in this paper are the same as in [1].

2 Structure of Norming hypergraph pairs 6 2.1 Two Hölder type inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Factorizable hypergraph pairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3 Semi-norming hypergraph pairs that are not norming . . . . . . . . . . . . . . . . . . . . 12 2.4 Some facts about Gowers norms . . . . . . . . . ....

We study leading-edge local search heuristics for balanced hypergraph partitioning and Boolean satisfiability, intending the generalization of such heuristics beyond their original domains. We adapt the Fiduccia Mattheyses (FM) hypergraph partitioning heuristic to Boolean Satisfiability (SAT), and the WalkSAT SAT solver to hypergraph partitioning. Focusing on balanced hypergraph partitioning, w...

Estimating the discrepancy of the hypergraph of all arithmetic progressions in the set [N ] = {1, 2, . . . , N} was one of the famous open problems in combinatorial discrepancy theory for a long time. An extension of this classical hypergraph is the hypergraph of sums of k (k ≥ 1 fixed) arithmetic progressions. The hyperedges of this hypergraph are of the form A1 + A2 + . . . + Ak in [N ], wher...

Using the Katona-Kierstead definition of a Hamiltonian cycle in a uniform hypergraph, we continue the investigation of the existence of a decomposition of the complete 3-uniform hypergraph into Hamiltonian cycles began by Bailey and Stevens. We also discuss two extensions of the problem: to the complete 3-uniform hypergraph from which a parallel class of triples has been removed, and to the com...

The paper considers the problem of computing a maximal independent set in a hypergraph (see 3] and 7]). We present an eecient deterministic NC algorithm for nding a maximal independent set in a hypergraph of dimension 3: the algorithm runs in time O(log 4 n) time on n + m processors of an EREW PRAM and is optimal up to a polylogarithmic factor. Our algorithm adapts the technique of Goldberg and...