scholarly journals Longest Paths in Random Hypergraphs

2021 ◽  
Vol 35 (4) ◽  
pp. 2430-2458
Author(s):  
Oliver Cooley ◽  
Frederik Garbe ◽  
Eng Keat Hng ◽  
Mihyun Kang ◽  
Nicolás Sanhueza-Matamala ◽  
...  
Keyword(s):  
Longest Paths ◽  
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

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

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
Sign in / Sign up

Export Citation Format

Share Document