We prove a hypergraph analogue of the Erdős-Gallai theorem: for any δ > 0 there exists n0 such that for any 0 ≤ α ≤ 1, any k-uniform hypergraph H on n ≥ n0 vertices with at least (α+ δ) ( n k ) edges contains a tight cycle of length at least αn. Moreover, H contains tight cycles of all lengths up to αn which are divisible by k. A key tool in our proof is a ‘regular slice lemma’, which is derive...

Recommender systems in online marketing websites like Amazon.com and CDNow.com suggest relevant services and favorite products to customers. In this paper, we proposed a novel hypergraph-based kernel computation combined with k nearest neighbor (kNN) to predict ratings of users. In this method, we change regular definition style of hypergraph diffusion kernel. Our comparative studies show that ...

Abstract. We present a new abstraction method for heap structures that is based on hyperedge replacement grammars. We use labeled hypergraphs as abstract representation of heap structures. A given hypergraph replacement grammar induces a set of concrete heap structures from a hypergraph. Our technique allows to abstract and concretize the heap partially. Thus the heap parts of high entropy can ...

A rate R = 5/20 hypergraph-based woven convolutional code with overall constraint length 67 and constituent convolutional codes is presented. It is based on a 3-partite, 3uniform, 4-regular hypergraph and contains rate R = 3/4 constituent convolutional codes with overall constraint length 5. Although the code construction is based on low-complexity codes, the free distance of this construction,...

We prove that the maximum number of edges in a k-uniform hypergraph on n vertices containing no 2-regular subhypergraph is ( n−1 k−1 ) if k ≥ 4 is even and n is sufficiently large. Equality holds only if all edges contain a specific vertex v. For odd k we conjecture that this maximum is ( n−1 k−1 ) + bn−1 k c, with equality only for the hypergraph described above plus a maximum matching omittin...

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...

We present a theoretical study of new families of stochastic complex information modules encoded in the hypergraph states which are defined by the fractional entropic descriptor. The essential connection between the Lyapunov exponents and d-regular hypergraph fractal set is elucidated. To further resolve the divergence in the complexity of classical and quantum representation of a hypergraph, w...

As is well known, Lovfisz Local Lemma implies that every d-uniform d-regular hyper-graph is 2-colorable, provided d > 9. We present a different proof of a slightly stronger result; every d-uniform d-regular hypergraph is 2-colorable, provided d > 8.

We show that the list chromatic number of a simple d-regular r-uniform hypergraph is at least (1/2r log(2r 2) + o(1)) log d if d is large.