منابع مشابه
Packing random graphs and hypergraphs
We determine to within a constant factor the threshold for the property that two random k-uniform hypergraphs with edge probability p have an edge-disjoint packing into the same vertex set. More generally, we allow the hypergraphs to have different densities. In the graph case, we prove a stronger result, on packing a random graph with a fixed graph.
متن کاملRandom Kneser graphs and hypergraphs
A Kneser graph KGn,k is a graph whose vertices are all k-element subsets of [n], with two vertices connected if and only if the corresponding sets do not intersect. A famous result due to Lovász states that the chromatic number of a Kneser graph KGn,k is equal to n − 2k + 2. In this paper we discuss the chromatic number of random Kneser graphs and hypergraphs. It was studied in two recent paper...
متن کاملPacking hamilton cycles in random and pseudo-random hypergraphs
We say that a k-uniform hypergraph C is a Hamilton cycle of type `, for some 1 ≤ ` ≤ k, if there exists a cyclic ordering of the vertices of C such that every edge consists of k consecutive vertices and for every pair of consecutive edges Ei−1, Ei in C (in the natural ordering of the edges) we have |Ei−1 \ Ei| = `. We prove that for k/2 < ` ≤ k, with high probability almost all edges of the ran...
متن کاملPacking perfect matchings in random hypergraphs
We introduce a new procedure for generating the binomial random graph/hypergraph models, referred to as online sprinkling. As an illustrative application of this method, we show that for any fixed integer k ≥ 3, the binomial k-uniform random hypergraph H n,p contains N := (1 − o(1)) ( n−1 k−1 ) p edge-disjoint perfect matchings, provided p ≥ log C n nk−1 , where C := C(k) is an integer dependin...
متن کاملDiscrepancy of random graphs and hypergraphs
The discrepancy of an n-vertex k-uniform hypergraph H with edge density ρH = e(H)/ ( n k ) is disc(H) = maxS⊆V (H) ∣∣∣e(S)− ρH(|S| k )∣∣∣, where e(S) = e(H[S]) is the number of edges in the sub-hypergraph induced by S. This important concept appears naturally in various branches of combinatorics and was studied by many researchers in recent years. The discrepancy can be viewed as a measure of h...
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ژورنال
عنوان ژورنال: Random Structures & Algorithms
سال: 2016
ISSN: 1042-9832,1098-2418
DOI: 10.1002/rsa.20673