Results 21 to 30 of about 11,596 (195)
Almost Self-Complementary Uniform Hypergraphs
Discussiones Mathematicae Graph Theory, 2018 A k-uniform hypergraph (k-hypergraph) is almost self-complementary if it is isomorphic with its complement in the complete k-uniform hypergraph minus one edge. We prove that an almost self-complementary k-hypergraph of order n exists if and only if (nk)$\
Wojda Adam Paweł
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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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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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High Girth Hypergraphs with Unavoidable Monochromatic or Rainbow Edges
Discussiones Mathematicae Graph Theory, 2022 A classical result of Erdős and Hajnal claims that for any integers k, r, g ≥ 2 there is an r-uniform hypergraph of girth at least g with chromatic number at least k.
Axenovich Maria, Karrer Annette
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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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Transversals in 4-Uniform Hypergraphs
The Electronic Journal of Combinatorics, 2016 Let $H$ be a $4$-uniform hypergraph on $n$ vertices. The transversal number $\tau(H)$ of $H$ is the minimum number of vertices that intersect every edge. The result in [J. Combin. Theory Ser. B 50 (1990), 129—133] by Lai and Chang implies that $\tau(H) \le 7n/18$ when $H$ is $3$-regular. The main result in [Combinatorica 27 (2007), 473—487] by Thomassé
Michael A. Henning, Anders Yeo
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Kneser Colorings of Uniform Hypergraphs [PDF]
Electronic Notes in Discrete Mathematics, 2009 Abstract For fixed positive integers r, k and l with l r , and an r-uniform hypergraph H, let κ ( H , k , l ) denote the number of k-colorings of the set of hyperedges of H for which any two hyperedges in the same color class intersect in at least l vertices. Consider the function KC ( n , r , k , l ) = max H ∈
Carlos Hoppen +2 more
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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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The Existence of Quasi Regular and Bi-Regular Self-Complementary 3-Uniform Hypergraphs
Discussiones Mathematicae Graph Theory, 2016 A k-uniform hypergraph H = (V ;E) is called self-complementary if there is a permutation σ : V → V , called a complementing permutation, such that for every k-subset e of V , e ∈ E if and only if σ(e) ∉ E. In other words, H is isomorphic with H′ = (V ; V(
Kamble Lata N. +2 more
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Cyclic Partitions of Complete and Almost Complete Uniform Hypergraphs
Discussiones Mathematicae Graph Theory, 2022 We consider cyclic partitions of the complete k-uniform hypergraph on a finite set V, minus a set of s edges, s ≥ 0. An s-almost t-complementary k-hypergraph is a k-uniform hypergraph with vertex set V and edge set E for which there exists a permutation ...
Dilbarjot, Gosselin Shonda Dueck
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