Results 11 to 20 of about 418 (155)
Maximum Hypergraphs without Regular Subgraphs
Discussiones Mathematicae Graph Theory, 2014 We show that an n-vertex hypergraph with no r-regular subgraphs has at most 2n−1+r−2 edges. We conjecture that if n > r, then every n-vertex hypergraph with no r-regular subgraphs having the maximum number of edges contains a full star, that is, 2n−1 ...
Kim Jaehoon, Kostochka Alexandr V.
doaj +2 more sources
Spectra of Random Regular Hypergraphs [PDF]
The Electronic Journal of Combinatorics, 2021 In this paper, we study the spectra of regular hypergraphs following the definitions from Feng and Li (1996). Our main result is an analog of Alon's conjecture for the spectral gap of the random regular hypergraphs. We then relate the second eigenvalues to both its expansion property and the mixing rate of the non-backtracking random walk on regular ...
Ioana Dumitriu, Yizhe Zhu
openaire +3 more sources
Regular slices for hypergraphs [PDF]
Electronic Notes in Discrete Mathematics, 2015 Abstract We present a ‘Regular Slice Lemma’ which, given a k-graph G , returns a regular ( k − 1 ) -complex J with respect to which G has useful regularity properties. We believe that many arguments in extremal hypergraph theory are made considerably simpler by using this lemma rather than existing forms of the Strong ...
Peter Allen 0001 +3 more
openaire +3 more sources
On characterizing hypergraph regularity [PDF]
Random Structures & Algorithms, 2002 AbstractSzemerédi's Regularity Lemma is a well‐known and powerful tool in modern graph theory. This result led to a number of interesting applications, particularly in extremal graph theory. A regularity lemma for 3‐uniform hypergraphs developed by Frankl and Rödl [8] allows some of the Szemerédi Regularity Lemma graph applications to be extended to ...
Y. Dementieva +3 more
openaire +1 more source
An Algorithmic Hypergraph Regularity Lemma [PDF]
Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, 2015 AbstractSzemerédi 's Regularity Lemma is a powerful tool in graph theory. It asserts that all large graphs admit bounded partitions of their edge sets, most classes of which consist of uniformly distributed edges. The original proof of this result was nonconstructive, and a constructive proof was later given by Alon, Duke, Lefmann, Rödl, and Yuster ...
Brendan Nagle +2 more
openaire +2 more sources
On Regular Hypergraphs of High Girth [PDF]
The Electronic Journal of Combinatorics, 2014 We give lower bounds on the maximum possible girth of an $r$-uniform, $d$-regular hypergraph with at most $n$ vertices, using the definition of a hypergraph cycle due to Berge. These differ from the trivial upper bound by an absolute constant factor (viz., by a factor of between $3/2+o(1)$ and $2 +o(1)$).
ELLIS, DC, Linial, N
openaire +3 more sources
Approximate counting of regular hypergraphs [PDF]
Information Processing Letters, 2013 In this paper we asymptotically count d-regular k-uniform hypergraphs on n vertices, provided k is fixed and d=d(n)=o(n1/2). In doing so, we extend to hypergraphs a switching technique of McKay and Wormald.
Andrzej Dudek +3 more
openaire +2 more sources
Transversals in regular uniform hypergraphs
Journal of Graph Theory, 2023 AbstractThe transversal number of a hypergraph is the minimum number of vertices that intersect every edge of . This notion of transversal is fundamental in hypergraph theory and has been studied a great deal in the literature. A hypergraph is ‐regular if every vertex of has degree , that is, every vertex of belongs to exactly edges. Further, is
Michael A. Henning, Anders Yeo
openaire +2 more sources
Hypergraph regularity and random sampling
Random Structures & Algorithms, 2023 AbstractSuppose that a ‐uniform hypergraph satisfies a certain regularity instance (that is, there is a partition of given by the hypergraph regularity lemma into a bounded number of quasirandom subhypergraphs of prescribed densities). We prove that with high probability a large enough uniform random sample of the vertex set of also admits the same ...
Felix Joos +3 more
openaire +3 more sources
Weak hypergraph regularity and linear hypergraphs
Journal of Combinatorial Theory, Series B, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yoshiharu Kohayakawa +3 more
openaire +2 more sources