Results 71 to 80 of about 11,526 (190)
A Cheeger Cut for Uniform Hypergraphs [PDF]
Graphs and Combinatorics, 2021 AbstractThe graph Cheeger constant and Cheeger inequalities are generalized to the case of hypergraphs whose edges have the same cardinality. In particular, it is shown that the second largest eigenvalue of the generalized normalized Laplacian is bounded both above and below by the generalized Cheeger constant, and the corresponding eigenfunctions can ...
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Discrepancy of arithmetic progressions in boxes and convex bodies
Mathematika, Volume 72, Issue 2, April 2026.Abstract The combinatorial discrepancy of arithmetic progressions inside [N]:={1,…,N}$[N]:= \lbrace 1, \ldots, N\rbrace$ is the smallest integer D$D$ for which [N]$[N]$ can be colored with two colors so that any arithmetic progression in [N]$[N]$ contains at most D$D$ more elements from one color class than the other.
Lily Li, Aleksandar Nikolov
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Hamilton ℓ-cycles in uniform hypergraphs
Journal of Combinatorial Theory, Series A, 2010 v3: corrected very minor error in Lemma 4.6 and the proof of Lemma 6 ...
Kühn, Daniela +2 more
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f$f$‐Diophantine sets over finite fields via quasi‐random hypergraphs from multivariate polynomials
Mathematika, Volume 72, Issue 2, April 2026.Abstract We investigate f$f$‐Diophantine sets over finite fields via new explicit constructions of families of quasi‐random hypergraphs from multivariate polynomials. In particular, our construction not only offers a systematic method for constructing quasi‐random hypergraphs but also provides a unified framework for studying various hypergraphs ...
Seoyoung Kim, Chi Hoi Yip, Semin Yoo
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Book free 3-uniform hypergraphs
Discrete MathematicsA $k$-book in a hypergraph consists of $k$ Berge triangles sharing a common edge. In this paper we prove that the number of the hyperedges in a $k$-book-free 3-uniform hypergraph on $n$ vertices is at most $\frac{n^2}{8}(1+o(1))$.
Debarun Ghosh +5 more
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Cognitive Networks for Knowledge Modeling: A Gentle Introduction for Data‐ and Cognitive Scientists
WIREs Cognitive Science, Volume 17, Issue 2, March/April 2026.Cognitive network science helps organize associative knowledge—that is, the connections between concepts. These connections play a key role in cognitive processes such as language understanding and context interpretation, even though they are not obvious in language use.
Edith Haim, Massimo Stella
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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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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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Zarankiewicz bounds from distal regularity lemma
Bulletin of the London Mathematical Society, Volume 58, Issue 3, March 2026.Abstract Since Kővári, Sós and Turán proved upper bounds for the Zarankiewicz problem in 1954, much work has been undertaken to improve these bounds, and some have done so by restricting to particular classes of graphs. In 2017, Fox, Pach, Sheffer, Suk and Zahl proved better bounds for semialgebraic binary relations, and this work was extended by Do in
Mervyn Tong
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Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract Heilbronn's triangle problem is a classical question in discrete geometry. It asks to determine the smallest number Δ=Δ(N)$\Delta = \Delta (N)$ for which every collection in N$N$ points in the unit square spans a triangle with area at most Δ$\Delta$.
Dmitrii Zakharov
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