Cores of random r-partite hypergraphs

Cores of random r-partite hypergraphs

We show that the threshold cr,k for appearance of a k-core in a random r-partite r-uniform hypergraph Gr,n,m is the same as for a random r-uniform hypergraph with cn/r edges without the r-partite restriction, where r, k ≥ 2. In both cases, the average degree is c. This is an important problem in the analysis of the algorithm presented in [2]. The algorithm constructs a family of minimal perfect...

Coverings and matchings in r-partite hypergraphs

Ryser’s conjecture postulates that, for r-partite hypergraphs, τ ≤ (r − 1)ν where τ is the covering number of the hypergraph and ν is the matching number. Although this conjecture has been open since the 1960s, researchers have resolved it for special cases such as for intersecting hypergraphs where r ≤ 5. In this paper, we prove several results pertaining to matchings and coverings in r-partit...

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...

Ramsey Properties of Random k-Partite, k-Uniform Hypergraphs

We investigate the threshold probability for the property that every r-coloring of the edges of a random binomial k-uniform hypergraph G(k)(n, p) yields a monochromatic copy of some fixed hypergraph G. In this paper we solve the problem for arbitrary k ≥ 3 and k-partite, k-uniform hypergraphs G.

The cores of random hypergraphs with a given degree sequence