Let p(k) denote the partition function of k. For each k ≥ 2, we describe a list of p(k) − 1 quasirandom properties that a k-uniform hypergraph can have. Our work connects previous notions on hypergraph quasirandomness, beginning with the early work of Chung and Graham and Frankl-Rödl related to strong hypergraph regularity, the spectral approach of Friedman-Wigderson, and more recent results of...

An oriented hypergraph is a hypergraph where each vertex-edge incidence is given a label of +1 or −1. The adjacency and Laplacian eigenvalues of an oriented hypergraph are studied. Eigenvalue bounds for both the adjacency and Laplacian matrices of an oriented hypergraph which depend on structural parameters of the oriented hypergraph are found. An oriented hypergraph and its incidence dual are ...

Recent years have witnessed a surge of interest in hypergraph-based transductive image classification. Hypergraph-based transductive learning models the high-order relationship of samples by using a hyperedge to link multiple samples. In order to extend the high-order relationship of samples, we incorporate linear correlation of sparse representation to hypergraph learning framework to improve ...

In this work we show the de ciencies of the graph model for decomposing sparse matrices for parallel matrix vector multiplica tion Then we propose two hypergraph models which avoid all de cien cies of the graph model The proposed models reduce the decomposition problem to the well known hypergraph partitioning problem widely en countered in circuit partitioning in VLSI We have implemented fast ...

The paper considers two decision problems on hypergraphs, hypergraph saturation and recognition of the transversal hypergraph, and discusses their significance for several search problems in applied computer science. Hypergraph saturation, i.e., given a hypergraph H, decide if every subset of vertices is contained in or contains some edge of H, is shown to be co-NP-complete. A certain subproble...

We consider a class of hypergraphs called hypercycles and we show that a hypercycle $C_n^{d,alpha}$ is shellable or sequentially the Cohen--Macaulay if and only if $nin{3,5}$. Also, we characterize Cohen--Macaulay hypercycles. These results are hypergraph versions of results proved for cycles in graphs.