Results 31 to 40 of about 730,755 (216)
On the Sizes of (k, l)-Edge-Maximal r-Uniform Hypergraphs
Discussiones Mathematicae Graph Theory, 2023 Let H = (V, E) be a hypergraph, where V is a set of vertices and E is a set of non-empty subsets of V called edges. If all edges of H have the same cardinality r, then H is an r-uniform hypergraph; if E consists of all r-subsets of V, then H is a ...
Tian Yingzhi +3 more
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Uniform hypergraphs containing no grids [PDF]
, 2013 A hypergraph is called an r×r grid if it is isomorphic to a pattern of r horizontal and r vertical lines, i.e.,a family of sets {A1, ..., Ar, B1, ..., Br} such that Ai∩Aj=Bi∩Bj=φ for 1 ...
Füredi, Zoltán, Ruszinkó, Miklós
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Hypergraph Turán Problems in ℓ2-Norm [PDF]
, 2022 There are various different notions measuring extremality of hypergraphs. In this survey we compare the recently introduced notion of the codegree squared extremal function with the Turán function, the minimum codegree threshold and the uniform Turán ...
Clemen, Felix Christian +2 more
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Tight Euler tours in uniform hypergraphs - computational aspects [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 By a tight tour in a $k$-uniform hypergraph $H$ we mean any sequence of its vertices $(w_0,w_1,\ldots,w_{s-1})$ such that for all $i=0,\ldots,s-1$ the set $e_i=\{w_i,w_{i+1}\ldots,w_{i+k-1}\}$ is an edge of $H$ (where operations on indices are computed ...
Zbigniew Lonc +2 more
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Spectra of uniform hypergraphs
Linear Algebra and its Applications, 2012 We present a spectral theory of hypergraphs that closely parallels Spectral Graph Theory. A number of recent developments building upon classical work has led to a rich understanding of "hyperdeterminants" of hypermatrices, a.k.a. multidimensional arrays.
Cooper, Joshua, Dutle, Aaron
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Hypergraph expanders of all uniformities from Cayley graphs
, 2021 Hypergraph expanders are hypergraphs with surprising, non‐intuitive expansion properties. In a recent paper, the first author gave a simple construction, which can be randomized, of 3‐uniform hypergraph expanders with polylogarithmic degree.
Tidor, Jonathan +2 more
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The Lagrangian Density of {123, 234, 456} and the Turán Number of its Extension
Discussiones Mathematicae Graph Theory, 2021 Given a positive integer n and an r-uniform hypergraph F, the Turán number ex(n, F ) is the maximum number of edges in an F -free r-uniform hypergraph on n vertices.
Chen Pingge, Liang Jinhua, Peng Yuejian
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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
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Hypergraph regularity and higher arity VC-dimension [PDF]
, 2020 We generalize the fact that graphs with small VC-dimension can be approximated by rectangles, showing that hypergraphs with small VC_k-dimension (equivalently, omitting a fixed finite (k+1)-partite (k+1)-uniform hypergraph) can be approximated by k-ary ...
Chernikov, Artem, Towsner, Henry
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Journal of Inequalities and Applications, 2020 In this paper, we obtain a sharp upper bound on the spectral radius of a nonnegative k-uniform tensor and characterize when this bound is achieved. Furthermore, this result deduces the main result in [X. Duan and B.
Chuang Lv, Lihua You, Xiao-Dong Zhang
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