Results 91 to 100 of about 730,755 (216)
Equivalence between Erdős–Hajnal and polynomial Rödl and Nikiforov conjectures
Bulletin of the London Mathematical Society, Volume 58, Issue 10, October 2026.Abstract It is well‐known that polynomial versions of theorems of Rödl and Nikiforov, as conjectured by Fox and Sudakov and Nguyen, Scott and Seymour imply the classical Erdős–Hajnal conjecture. In this note, we prove that these three conjectures are in fact equivalent, extending several previous particular results in this direction by Fox, Nguyen ...
Matija Bucić, Jacob Fox, Huy Tuan Pham
wiley +1 more source
Unsupervised hyperlink prediction based on hypergraph random walk
Complex & Intelligent SystemsConventional link prediction methods mainly aim to estimate pairwise relationships between nodes in graph structures, typically addressing single-type interactions.
Yanlin Yang +5 more
doaj +1 more source
Super edge-magic labeling of m-node k-uniform hyperpaths and m-node k-uniform hypercycles
AKCE International Journal of Graphs and Combinatorics, 2016 We generalize the notion of the super edge-magic labeling of graphs to the notion of the super edge-magic labeling of hypergraphs. For a hypergraph H with a finite vertex set V and a hyperedge set E, a bijective function f:V∪E→{1,2,3,…,|V|+|E|} is called
Ratinan Boonklurb +2 more
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No‐(k+1)$(k+1)$‐in‐line problem for large constant k$k$
Bulletin of the London Mathematical Society, Volume 58, Issue 10, October 2026.Abstract How many points can be placed in an n×n$n\times n$ grid so that every (affine) line contains at most k$k$ points? We prove that for n⩾k⩾1037$n \geqslant k \geqslant 10^{37}$ the maximum number of points is exactly kn$kn$. Our proof builds on the recent work of Kovács, Nagy and Szabó (who proved an analogous result when k$k$ is at least about ...
Alexandr Grebennikov, Matthew Kwan
wiley +1 more source
Monochromatic loose paths in multicolored $k$-uniform cliques [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 For integers $k\ge 2$ and $\ell\ge 0$, a $k$-uniform hypergraph is called a loose path of length $\ell$, and denoted by $P_\ell^{(k)}$, if it consists of $\ell $ edges $e_1,\dots,e_\ell$ such that $|e_i\cap e_j|=1$ if $|i-j|=1$ and $e_i\cap e_j=\emptyset$
Andrzej Dudek, Andrzej Ruciński
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Bounded diameter monochromatic component covers
Mathematika, Volume 72, Issue 4, October 2026.Abstract Ryser conjectured that every r$r$‐edge‐coloured complete graph can be covered by r−1$r-1$ monochromatic trees. Motivated by a question of Austin in analysis, Milićević predicted something stronger — that every r$r$‐edge‐coloured complete graph can be covered by r−1$r-1$ monochromatic trees of bounded diameter.
Alexey Pokrovskiy
wiley +1 more source
The maximum Wiener index of a uniform hypergraph
, 2023 The Wiener index of a (hyper)graph is calculated by summing up the distances between all pairs of vertices. We determine the maximum possible Wiener index of a connected $n$-vertex $k$-uniform hypergraph and characterize for every~$n$ all hypergraphs ...
Tuite, James +4 more
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3-uniform hypergraphs and linear cycles [PDF]
Electronic Notes in Discrete Mathematics, 2017 Improved the writing, more explanation added and corrections ...
Beka Ergemlidze +2 more
openaire +5 more sources
Families of triples with high minimum degree are hamiltonian
Discussiones Mathematicae Graph Theory, 2014 In this paper we show that every family of triples, that is, a 3-uniform hypergraph, with minimum degree at least contains a tight Hamiltonian ...
Rödl Vojtech, Ruciński Andrzej
doaj +1 more source
EIGENVALUES AND LINEAR QUASIRANDOM HYPERGRAPHS
Forum of Mathematics, Sigma, 2015 Let $p(k)$ denote the partition function of $k$. For each $k\geqslant 2$, we describe a list of $p(k)-1$ quasirandom properties that a $k$-uniform hypergraph can have. Our work connects previous notions on linear hypergraph quasirandomness by Kohayakawa,
JOHN LENZ, DHRUV MUBAYI
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