Regular uniform hypergraphs, s -cycles, s -paths and their largest Laplacian H-eigenvalues

Regular Uniform Hypergraphs, s-Cycles, s-Paths and Their largest Laplacian H-Eigenvalues∗

In this paper, we show that the largest signless Laplacian H-eigenvalue of a connected k-uniform hypergraph G, where k ≥ 3, reaches its upper bound 2∆(G), where ∆(G) is the largest degree of G, if and only if G is regular. Thus the largest Laplacian H-eigenvalue of G, reaches the same upper bound, if and only if G is regular and oddbipartite. We show that an s-cycle G, as a k-uniform hypergraph...

Perfect Matchings in Random r-regular, s-uniform Hypergraphs

The copyright law of the United States (title 17, U.S. Code) governs the making of photocopies or other reproductions of copyrighted material. Any copying of this document without permission of its author may be prohibited by law. Perfect matchings in random i—regular, 5—uniform hypergraphs.

Rainbow H-Factors of Complete s-Uniform r-Partite Hypergraphs

We say a s-uniform r-partite hypergraph is complete, if it has a vertex partition {V1, V2, . . . , Vr} of r classes and its hyperedge set consists of all the s-subsets of its vertex set which have at most one vertex in each vertex class. We denote the complete s-uniform r-partite hypergraph with k vertices in each vertex class by Ts,r(k). In this paper we prove that if h, r and s are positive i...

Laplacian eigenvalues and partition problems in hypergraphs

We use the generalization of the Laplacian matrix to hypergraphs to obtain several spectral-like results on partition problems in hypergraphs which are computationally difficult to solve (NP-hard or NP-complete). Therefore it is very important to obtain nontrivial bounds. More precisely, the following parameters are bounded in the paper: bipartition width, averaged minimal cut, isoperimetric nu...

Perfect Matchings in Random s-Uniform Hypergraphs