Two-coloring random hypergraphs

2002 ◽  
Vol 20 (2) ◽  
pp. 249-259 ◽  
Author(s):  
Dimitris Achlioptas ◽  
Jeong Han kim ◽  
Michael Krivelevich ◽  
Prasad Tetali
Keyword(s):  
Random Hypergraphs

Panchromatic colorings of random hypergraphs

2021 ◽  
Vol 31 (1) ◽  
pp. 19-41
Author(s):  
D. A. Kravtsov ◽  
N. E. Krokhmal ◽  
D. A. Shabanov
Keyword(s):  
Binomial Model ◽  
Threshold Probability ◽  
The Difference ◽  
Random Hypergraphs

Abstract We study the threshold probability for the existence of a panchromatic coloring with r colors for a random k-homogeneous hypergraph in the binomial model H(n, k, p), that is, a coloring such that each edge of the hypergraph contains the vertices of all r colors. It is shown that this threshold probability for fixed r < k and increasing n corresponds to the sparse case, i. e. the case p = c n / ( n k ) $p = cn/{n \choose k}$ for positive fixed c. Estimates of the form c 1(r, k) < c < c 2(r, k) for the parameter c are found such that the difference c 2(r, k) − c 1(r, k) converges exponentially fast to zero if r is fixed and k tends to infinity.

On Spanning Structures in Random Hypergraphs

2015 ◽  
Vol 49 ◽  
pp. 611-619 ◽  
Author(s):  
O. Parczyk ◽  
Y. Person
Keyword(s):  
Random Hypergraphs

scholarly journals The Multiple-Orientability Thresholds for Random Hypergraphs

2015 ◽  
Vol 25 (6) ◽  
pp. 870-908 ◽  
Author(s):  
NIKOLAOS FOUNTOULAKIS ◽  
MEGHA KHOSLA ◽  
KONSTANTINOS PANAGIOTOU
Keyword(s):  
Load Balancing ◽  
Hard Disk ◽  
Maximum Load ◽  
Disk Arrays ◽  
Uniform Hypergraph ◽  
Cuckoo Hashing ◽  
Uniform Hypergraphs ◽  
Random Hypergraphs ◽  
Do So ◽  
Parallel Access

Ak-uniform hypergraphH= (V, E) is called ℓ-orientable if there is an assignment of each edgee∈Eto one of its verticesv∈esuch that no vertex is assigned more than ℓ edges. LetHn,m,kbe a hypergraph, drawn uniformly at random from the set of allk-uniform hypergraphs withnvertices andmedges. In this paper we establish the threshold for the ℓ-orientability ofHn,m,kfor allk⩾ 3 and ℓ ⩾ 2, that is, we determine a critical quantityc*k,ℓsuch that with probability 1 −o(1) the graphHn,cn,khas an ℓ-orientation ifc<c*k,ℓ, but fails to do so ifc>c*k,ℓ.Our result has various applications, including sharp load thresholds for cuckoo hashing, load balancing with guaranteed maximum load, and massive parallel access to hard disk arrays.

scholarly journals Short paths in 3-uniform quasi-random hypergraphs

2004 ◽  
Vol 24 (3) ◽  
pp. 469 ◽  
Author(s):  
Joanna Polcyn
Keyword(s):  
Random Hypergraphs

scholarly journals Loose Cores and Cycles in Random Hypergraphs

2021 ◽  
pp. 280-285
Author(s):  
Oliver Cooley ◽  
Mihyun Kang ◽  
Julian Zalla
Keyword(s):  
Random Hypergraphs

scholarly journals Cache-Oblivious Peeling of Random Hypergraphs

2014 ◽  
Author(s):  
Djamal Belazzougui ◽  
Paolo Boldi ◽  
Giuseppe Ottaviano ◽  
Rossano Venturini ◽  
Sebastiano Vigna
Keyword(s):  
Random Hypergraphs ◽  
Cache Oblivious

Hypernetwork models based on random hypergraphs

2019 ◽  
Vol 30 (08) ◽  
pp. 1950052
Author(s):  
Feng Hu ◽  
Jin-Li Guo ◽  
Fa-Xu Li ◽  
Hai-Xing Zhao
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
World Systems ◽  
Uniform Hypergraphs ◽  
Different Types ◽  
Powerful Means ◽  
Simulation Results ◽  
Parameter Values ◽  
Random Hypergraphs

Hypernetworks are ubiquitous in real-world systems. They provide a powerful means of accurately depicting networks of different types of entity and will attract more attention from researchers in the future. Most previous hypernetwork research has been focused on the application and modeling of uniform hypernetworks, which are based on uniform hypergraphs. However, random hypernetworks are generally more common, therefore, it is useful to investigate the evolution mechanisms of random hypernetworks. In this paper, we construct three dynamic evolutional models of hypernetworks, namely the equal-probability random hypernetwork model, the Poisson-probability random hypernetwork model and the certain-probability random hypernetwork model. Furthermore, we analyze the hyperdegree distributions of the three models with mean-field theory, and we simulate each model numerically with different parameter values. The simulation results agree well with the results of our theoretical analysis, and the findings indicate that our models could help understand the structure and evolution mechanisms of real systems.

scholarly journals On Erdős–Ko–Rado for Random Hypergraphs II

2018 ◽  
Vol 28 (1) ◽  
pp. 61-80 ◽  
Author(s):  
A. HAMM ◽  
J. KAHN
Keyword(s):  
Sperner's Theorem ◽  
Random Hypergraphs

Denote by ${\mathcal H}_k$(n, p) the random k-graph in which each k-subset of {1,. . .,n} is present with probability p, independent of other choices. More or less answering a question of Balogh, Bohman and Mubayi, we show: there is a fixed ε > 0 such that if n = 2k + 1 and p > 1 - ε, then w.h.p. (that is, with probability tending to 1 as k → ∞), ${\mathcal H}_k$(n, p) has the ‘Erdős–Ko–Rado property’. We also mention a similar random version of Sperner's theorem.

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