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Perfect matchings in random uniform hypergraphs
2003
Random structures & algorithms (Print)
In the random k-uniform hypergraph H k (n, p) on a vertex set V of size n, each subset of size k of V independently belongs to it with probability p. ...
Motivated by a theorem of Erdős and Rényi [6] regarding when a random graph G(n, p) = H 2 (n, p) has a perfect matching, Schmidt and Shamir [14] essentially conjectured the following. ...
Molloy and Reed [5] found the exact constant c k (for a fixed k) so that with high probability the random d-regular k-uniform hypergraph has a perfect matching if d ≥ c k , otherwise no perfect matching ...
doi:10.1002/rsa.10093
fatcat:gpg2554bzndjdm3j77fthaug2i
Almost perfect matchings in random uniform hypergraphs
1997
Discrete Mathematics
A random r-uniform hypergraph ~r(n,p) is an r-uniform hypergraph with vertex set V of size IV] =n, in which each r-subset of V is chosen to be an edge of H E orgy(n, p) with probability p (where p may ...
One of the central problems in probabilistic combinatorics is that of determining the minimal probability p= p(n), for which a random hypergraph H c ~(n, p) has whpla perfect matching (assuming of course ...
matching in an r-uniform hypergraph. ...
doi:10.1016/s0012-365x(96)00310-x
fatcat:szu7yi5oo5gvritltfiqiuvfxu
Perfect Matchings in Random r-regular, s-uniform Hypergraphs
1996
Combinatorics, probability & computing
Perfect matchings in random s-uniform hypergraphs
2018
Cooper, Frieze, Molloy and Reed [5] considered the problem of perfect matchings in random r-regular, s-uniform hypergraphs. ...
A set of edges M = {X{ : i € /} is a perfect matching if (i) ijLje.1 implies X{ n Xj• = 0, and In this paper we consider the question of whether a random s-uniform hypergraph contains a perfect matching ...
doi:10.1184/r1/6479120
fatcat:ynmkw4fgqrbxpllgfzh5kxbzpa
Perfect matchings in random r-regular, s-uniform hypergraphs
2018
Thus if F is simple it has a perfect matching if and only if 7(F) has a perfect matching. ...
Let Q = Q(n,r,s) = {G = (V,E) : G is r-regular and 5-uniform }. Let G = G n ,r,s be chosen uniformly at random from Q. ...
doi:10.1184/r1/6479114.v1
fatcat:y6rko6s36rdqbosh7orlzo3sri
Matchings and Hamilton cycles in hypergraphs
2005
Discrete Mathematics & Theoretical Computer Science
International audience It is well known that every bipartite graph with vertex classes of size $n$ whose minimum degree is at least $n/2$ contains a perfect matching. ...
We prove an analogue of this result for uniform hypergraphs. ...
This in turn uses a probabilistic argument based on results about random perfect matchings in pseudo-random graphs [KOc] . ...
doi:10.46298/dmtcs.3457
fatcat:bkevf5myg5b3vmf7e63fg4qquu
Cycles and Matchings in Randomly Perturbed Digraphs and Hypergraphs
2016
Combinatorics, probability & computing
First, we prove that adding linearly many random edges to a densek-uniform hypergraph ensures the (asymptotically almost sure) existence of a perfect matching or a loose Hamilton cycle. ...
We give several results showing that different discrete structures typically gain certain spanning substructures (in particular, Hamilton cycles) after a modest random perturbation. ...
In particular, a k-uniform tight cycle is a k-uniform hypergraph with a cyclic ordering on its vertices such that every k consecutive vertices form an edge. ...
doi:10.1017/s0963548316000079
fatcat:dml2uezejjfpxlvs4oh5jb7dy4
Cycles and matchings in randomly perturbed digraphs and hypergraphs
2015
Electronic Notes in Discrete Mathematics
Our first theorem is that adding linearly many random edges to a dense k-uniform hypergraph typically ensures the existence of a perfect matching or a loose Hamilton cycle. ...
In these situations we show that the extremal examples are "fragile" in that after a modest random perturbation our desired substructures will typically appear. ...
In particular, a k-uniform tight cycle is a k-uniform hypergraph with a cyclic ordering on its vertices such that every k consecutive vertices form an edge. ...
doi:10.1016/j.endm.2015.06.027
fatcat:oesh5dzmxvdmxg3khfoyp5u3ly
Matchings in hypergraphs of large minimum degree
2006
Journal of Graph Theory
We also prove several related results which guarantee the existence of almost perfect matchings in r-uniform hypergraphs of large minimum degree. ...
It is well known that every bipartite graph with vertex classes of size n whose minimum degree is at least n/2 contains a perfect matching. We prove an analogue of this result for hypergraphs. ...
For random r-uniform hypergraphs, the threshold for a perfect matching is still not known. There are several partial results, see e.g. Kim [11] . ...
doi:10.1002/jgt.20139
fatcat:kygxhzl33vgqdjiutfnt2bwple
Co-degrees resilience for perfect matchings in random hypergraphs
[article]
2019
arXiv
pre-print
In this paper we prove an optimal co-degrees resilience property for the binomial k-uniform hypergraph model H_n,p^k with respect to perfect matchings. ...
) at least (1/2+o(1))np contains a perfect matching. ...
We are grateful to the referees for their valuable comments which were instrumental in revising this paper. ...
arXiv:1908.01435v1
fatcat:fgg2s65pfvgqhbne3lsaj5am2u
Co-degrees Resilience for Perfect Matchings in Random Hypergraphs
2020
Electronic Journal of Combinatorics
In this paper we prove an optimal co-degrees resilience property for the binomial $k$-uniform hypergraph model $H_{n,p}^k$ with respect to perfect matchings. ...
) at least $(1/2+o(1))np$ contains a perfect matching. ...
We are grateful to the referees for their valuable comments which were instrumental in revising this paper. ...
doi:10.37236/8167
fatcat:f7mshcirorggrc6b6rdunmmd7e
Perfect matchings in uniform hypergraphs with large minimum degree
2006
European journal of combinatorics (Print)
A perfect matching in a k-uniform hypergraph on n vertices, n divisible by k, is a set of n/k disjoint edges. ...
We prove that for every k ≥ 3 and sufficiently large n, a perfect matching exists in every n-vertex k-uniform hypergraph in which each set of k − 1 vertices is contained in n/2 + Ω (log n) edges. ...
In the case when r ≥ k − 2, Kühn and Osthus in [7] obtained an analogous result about almost perfect matchings in k-partite k-uniform hypergraphs. ...
doi:10.1016/j.ejc.2006.05.008
fatcat:6ixxrnuu35d65lzntcuas3uyqy
Loose Hamilton Cycles in Random 3-Uniform Hypergraphs
[article]
2010
arXiv
pre-print
In the random hypergraph H=H(n,p;3) each possible triple appears independently with probability p. A loose Hamilton cycle can be described as a sequence of edges x_i,y_i,x_i+1} for i=1,2,...,n/2. ...
Let Γ = Γ(X, Y, p) be the random 3-uniform hypergraph where each triple in Ω is independently included with probability p. ...
When ℓ = k − 1 we say that C is a loose Hamilton cycle and in this paper we will restrict our attention to loose Hamilton cycles in the random 3-uniform hypergraph H = H n,p;3 . ...
arXiv:1003.5817v1
fatcat:a7juufprtfh7rlyiranzdlnkcm
Distributed Algorithms for Matching in Hypergraphs
[article]
2020
arXiv
pre-print
In this model, we present the first three parallel algorithms for d-Uniform Hypergraph Matching, and we analyse them in terms of resources such as memory usage, rounds of communication needed, and approximation ...
We study the d-Uniform Hypergraph Matching (d-UHM) problem: given an n-vertex hypergraph G where every hyperedge is of size d, find a maximum cardinality set of disjoint hyperedges. ...
The first contains random uniform hypergraphs, and the second contains random geometric hypergraphs. Random Uniform Hypergraphs. ...
arXiv:2009.09605v1
fatcat:v7y2ldxi4fgbbjegtcubsjnzia
Page 604 of Mathematical Reviews Vol. , Issue 93b
[page]
1993
Mathematical Reviews
Intuitively, a “quasi-random” k-uniform hypergraph is one which has many of the properties associated with “almost all” k-uniform hypergraphs. ...
K. (1-BELL6) Quasi-random classes of hypergraphs. Random Structures Algorithms 1 (1990), no. 4, 363-382. ...
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