Results 161 to 170 of about 653 (189)

Embedding the Erdős–Rényi hypergraph into the random regular hypergraph and Hamiltonicity

Journal of Combinatorial Theory Series B, 2017
We establish an inclusion relation between two uniform models of random $k$-graphs (for constant $k \ge 2$) on $n$ labeled vertices: $\mathbb G^{(k)}(n,m)$, the random $k$-graph with $m$ edges, and $\mathbb R^{(k)}(n,d)$, the random $d$-regular $k$-graph. We show that if $n\log n\ll m\ll n^k$ we can choose $d = d(n) \sim {km}/n$ and couple $\mathbb G^{(
Andrzej Dudek, Alan Frieze, Andrzej Rucinski   +2 more
exaly   +4 more sources

An Algorithmic Regularity Lemma for Hypergraphs

SIAM Journal on Computing, 2000
Szemerédi's seminal ``regularity lemma'' is a powerful tool in extremal combinatorics and graph theory. Its algorithmic version (due to Alon et al.) has important applications to construct effective algorithms. This long and technically hard paper develops an analogous result for hypergraphs (which differs from other, earlier versions).
Andrzej Czygrinow, Vojtech Rödl
openaire   +2 more sources

On the Chromatic Number of Random Regular Hypergraphs

SIAM Journal on Discrete Mathematics
We estimate the likely values of the chromatic and independence numbers of the random $r$-uniform $d$-regular hypergraph on $n$ vertices for fixed $r$, large fixed $d$, and $n \rightarrow \infty$.
Patrick Bennett, Alan Frieze
exaly   +3 more sources

List Colourings of Regular Hypergraphs

Combinatorics, Probability and Computing, 2012
We show that the list chromatic number of a simpled-regularr-uniform hypergraph is at least (1/2rlog(2r2) +o(1)) logdifdis large.
David Saxton, Andrew Thomason 0001
openaire   +1 more source

Regularity Lemma for k‐uniform hypergraphs

Random Structures & Algorithms, 2004
AbstractSzemerédi's Regularity Lemma proved to be a very powerful tool in extremal graph theory with a large number of applications. Chung [Regularity lemmas for hypergraphs and quasi‐randomness, Random Structures Algorithms 2 (1991), 241–252], Frankl and Rödl [The uniformity lemma for hypergraphs, Graphs Combin 8 (1992), 309–312; Extremal problems on ...
Vojtech Rödl, Jozef Skokan
openaire   +1 more source

Two-regular subgraphs of odd-uniform hypergraphs

Journal of Combinatorial Theory Series B, 2018
Let be an odd integer and let n be a sufficiently large integer. We prove that the maximum number of edges in an n-vertex k-uniform hypergraph containing no 2-regular subgraphs is , and the equality holds if and only if H is a full k-star with center v ...
Jaehoon Kim
exaly   +2 more sources

Regularity lemmas for hypergraphs and quasi‐randomness

Random Structures & Algorithms, 1991
AbstractWe give a simple proof for Szemerédi's Regularity Lemma and its generalization for k‐uniform hypergraphs. For fixed k, there are altogether k ‐1 different versions of the regularity lemma for k‐uniform hypergraphs. The connection between regularity lemmas for hypergraphs and quasi‐random classes of hypergraphs is also investigated.
openaire   +2 more sources

Regular Representation of Finite Groups by Hypergraphs

Canadian Journal of Mathematics, 1978
All structures considered in this paper will be finite.The product στ of two permutations σ and τ of a set V is defined by στ(x) = στ(X)) for every x ∈ V. The set Sv of all permutations of F is a group under this operation. A permutation group on F is a subgroup of Sv.
Foldes, Stephane, Singhi, Navin M.
openaire   +2 more sources

Hypergraph regularized sparse feature learning

Neurocomputing, 2017
As an important pre-processing stage in many machine learning and pattern recognition domains, feature selection deems to identify the most discriminate features for a compact data representation. As typical feature selection methods, Lasso and its variants using the l1-norm based regularization have received much attention in recent years.
Mingxia Liu 0001, Jun Zhang 0018, Xiaochun Guo, Liujuan Cao   +3 more
openaire   +1 more source

An Edge Ordering Problem of Regular Hypergraphs

2006
Given a pair of integers 2≤s ≤k, define g s (k) to be the minimum integer such that, for any regular multiple hypergraph H =({1, ..., k}, {e 1, ..., e m }) with edge size at most s, there is a permutation π on {1, ..., m} (or edge ordering e π(1), ..., e \(_{\pi({\it m})}\))such that \(g(H, \pi) =\max\{ \max \{|d_{H_j}(u) - d_{H_j}(v)| : u, v\in e_{\pi(
Hongbing Fan, Robert Kalbfleisch
openaire   +1 more source