Results 61 to 70 of about 418 (155)

Regular subgraphs of uniform hypergraphs

Journal of Combinatorial Theory, Series B, 2016
We prove that for every integer $r\geq 2$, an $n$-vertex $k$-uniform hypergraph $H$ containing no $r$-regular subgraphs has at most $(1+o(1)){{n-1}\choose{k-1}}$ edges if $k\geq r+1$ and $n$ is sufficiently large. Moreover, if $r\in\{3,4\}$, $r\mid k$ and $k,n$ are both sufficiently large, then the maximum number of edges in an $n$-vertex $k$-uniform ...
openaire   +4 more sources

A Tight Bound for Hyperaph Regularity

Geometric and Functional Analysis, 2019
This manuscript contains the proof of the main result of arXiv:1907.07639 when specialized to 3-uniform ...
Moshkovitz, Guy, Shapira, Asaf
openaire   +5 more sources

New strong colouring of hypergraphs

Le Matematiche, 2011
We define a new colouring for a hypergraph, in particular for a graph. Such a method is a partition of the vertex-set of a hypergraph, in particular of a graph.
Sandro Rajola, Maria Scafati Tallini
doaj  

On Tight Tree‐Complete Hypergraph Ramsey Numbers

Journal of Graph Theory, Volume 113, Issue 1, Page 88-96, September 2026.
ABSTRACT Chvátal showed that for any tree T with k edges, the Ramsey number R ( T , n ) = k ( n − 1 ) + 1. For r = 3 or 4, we show that, if T is an r‐uniform nontrivial tight tree, then the hypergraph Ramsey number R ( T , n ) = Θ ( n r − 1 ). The 3‐uniform result comes from observing a construction of Cooper and Mubayi.
Jiaxi Nie
wiley   +1 more source

An Algorithmic Version of the Hypergraph Regularity Method [PDF]

SIAM Journal on Computing, 2005
Extending the Szemeredi regularity lemma for graphs, P. Frankl and V. Rodl [Random Structures Algorithms, 20 (2002), pp. 131-164] established a 3-graph regularity lemma triple systems ${\cal G}_n$ admit bounded partitions of their edge sets, most classes of which consist of regularly distributed triples.
Penny E. Haxell, Brendan Nagle, Vojtech Rödl   +2 more
openaire   +1 more source

Orientations of Graphs With at Most One Directed Path Between Every Pair of Vertices

Journal of Graph Theory, Volume 113, Issue 1, Page 143-164, September 2026.
ABSTRACT Given a graph G, we say that an orientation D of G is a KT orientation if, for all u , v ∈ V ( D ), there is at most one directed path (in any direction) between u and v. Graphs that admit such orientations have been used to construct graphs with large chromatic number and small clique number that served as counterexamples to various ...
Barbora Dohnalová, Jiří Kalvoda, Gaurav Kucheriya, Sophie Spirkl   +3 more
wiley   +1 more source

Regular Subgraphs of Linear Hypergraphs

International Mathematics Research Notices
Abstract We prove that the maximum number of edges in a 3-uniform linear hypergraph on $n$ vertices containing no 2-regular subhypergraph is $n^{1+o(1)}$. This resolves a conjecture of Dellamonica, Haxell, Łuczak, Mubayi, Nagle, Person, Rödl, Schacht, and Verstraëte.
Janzer, Oliver, Sudakov, Benny, Tomon, István   +2 more
openaire   +5 more sources

Supervised Restricted Data Fusion With Common, Local, and Distinct Components

Journal of Chemometrics, Volume 40, Issue 8, August 2026.
ABSTRACT In multi‐block data, the dominant sources of variation are not always most relevant to a response of interest, meaning that purely exploratory decompositions may fail to recover subtle but important response‐associated structure. We introduce PESCAR, a supervised extension of Penalised Exponential Simultaneous Component Analysis (PESCA) that ...
Fred T. G. White, Geert Roelof van der Ploeg, Anna Heintz‐Buschart, Lemeng Dong, Harro J. Bouwmeester, Age K. Smilde, Johan A. Westerhuis   +6 more
wiley   +1 more source

Asymmetric Results About Graph Homomorphisms

Random Structures &Algorithms, Volume 69, Issue 1, August 2026.
ABSTRACT Many important results in extremal graph theory can be roughly summarized as “if a triangle‐free graph G$$ G $$ has certain properties, then it has a homomorphism to a triangle‐free graph Γ$$ \Gamma $$ of bounded size.” For example, bounds on homomorphism thresholds give such a statement if G$$ G $$ has sufficiently high minimum degree, and ...
Lior Gishboliner, Eoin Hurley, Yuval Wigderson   +2 more
wiley   +1 more source

The number of regular simplices in higher dimensions

Bulletin of the London Mathematical Society, Volume 58, Issue 8, August 2026.
Abstract We study the extremal function Sdk(n)$S^k_d(n)$, defined as the maximum number of regular (k−1)$(k-1)$‐simplices spanned by n$n$ points in Rd$\mathbb {R}^d$. For any fixed d⩾2k⩾6$d\geqslant 2k\geqslant 6$, we determine the asymptotic behavior of Sdk(n)$S^k_d(n)$ up to a lower‐order term.
Felix Christian Clemen, Adrian Dumitrescu, Dingyuan Liu   +2 more
wiley   +1 more source