Answering a question of RR odl and Thoma, we show that the Nibble Algorithm for nding a collection of disjoint edges covering almost all vertices in an almost regular, uniform hypergraph with negligible pair degrees can be derandomized and parallelized to run in polylog time on polynomially many parallel processors. In other words, the nearly-perfect packing problem on this class of hypergraphs...

The search for the smallest possible $d$-regular graph of girth $g$ has a long history, and is usually known as cage problem. This problem natural extension to hypergraphs, where we may ask number vertices in $d$-regular, $r$-uniform hypergraph given (Berge) $g$. We show that these two problems are fact very closely linked. By extending ideas Cayley graphs context, find hypergraphs various para...

Low-dimensional k-ary n-cubes have been popular in recent multicomputers. These networks, however, suffer from high switching delays due to their high message distance. To overcome this problem, Dally has proposed a variation, called express k-ary n-cubes, with express channels that allow non-local messages to partially bypass clusters of nodes within a dimension. K-ary n-cubes are graph topolo...

Codes on hypergraphs are an extension of the well-studied family of codes on bipartite graphs. Bilu and Hoory (2004) constructed an explicit family of codes on regular t-partite hypergraphs whose minimum distance improves earlier estimates of the distance of bipartite-graph codes. They also suggested a decoding algorithm for such codes and estimated its error-correcting capability. In this pape...

A subgraph of a hypergraph H is even if all its degrees are positive even integers, and b-bounded if it has maximum degree at most b. Let fb(n) denote the maximum number of edges in a linear nvertex 3-uniform hypergraph which does not contain a b-bounded even subgraph. In this paper, we show that if b ≥ 12, then n logn 3b log logn ≤ fb(n) ≤ Bn(logn) for some absolute constant B, thus establishi...

Let r be a fixed constant and let H be an r-uniform, D-regular hypergraph on N vertices. Assume further that D → ∞ as N → ∞ and that co-degrees of pairs of vertices in H are at most L where L = o(D/ log N). We consider the random greedy algorithm for forming a matching in H. We choose a matching at random by iteratively choosing edges uniformly at random to be in the matching and deleting all e...

We study the maximum cardinality of a pairwise-intersecting family of subsets of an n-set, or the size of the smallest set in such a family, under either of the assumptions that it is regular (as a hypergraph) or that it admits a transitive permutation group. Not surprisingly, results under the second assumption are stronger. We also give some results for 4-wise intersecting families under the ...

In this paper, we introduce certain concepts, including neutrosophic hypergraph, line graph of neutrosophic hypergraph, dual neutrosophic hypergraph, tempered neutrosophic hypergraph and transversal neutrosophic hypergraph. We illustrate these concepts by several examples and investigate some of interesting properties. Key-words: Neutrosophic hypergraph, Line graph of neutrosophic hypergraph, D...

A hypergraph H is simply a collection of subsets of a finite set, which we will always denote by V. Elements of V are called vertices and elements of H edges. A hypergraph is k-uniform (k-bounded) if each of its edges has size k (at most k). The degree in H of a vertex x is the number of edges containing x, and is denoted by d(x). Similarly, d(x,y) denotes the number of edges containing both of...

Abstract This chapter introduces three hypergraph computation paradigms, including intra-hypergraph computation, inter-hypergraph and structure computation. Intra-hypergraph representation aims to conduct learning of a hypergraph, where each subject is represented by its components. Inter-hypergraph vertices in the vertex hypergraph. Hypergraph prediction, which find connections among vertices....