Results 21 to 30 of about 11,526 (190)
Hamilton cycles in quasirandom hypergraphs [PDF]
, 2015 We show that, for a natural notion of quasirandomness in $k$-uniform hypergraphs, any quasirandom $k$-uniform hypergraph on $n$ vertices with constant edge density and minimum vertex degree $\Omega(n^{k-1})$ contains a loose Hamilton cycle.
Lenz, John +2 more
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Saturated r-uniform hypergraphs
Discrete Mathematics, 1991 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Erdős, Paul +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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Turán Problems on Non-Uniform Hypergraphs [PDF]
The Electronic Journal of Combinatorics, 2014 A non-uniform hypergraph $H=(V,E)$ consists of a vertex set $V$ and an edge set $E\subseteq 2^V$; the edges in $E$ are not required to all have the same cardinality. The set of all cardinalities of edges in $H$ is denoted by $R(H)$, the set of edge types.
Johnston, J. Travis, Lu, Linyuan
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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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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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Covering complete partite hypergraphs by monochromatic components [PDF]
, 2016 A well-known special case of a conjecture attributed to Ryser states that k-partite intersecting hypergraphs have transversals of at most k-1 vertices. An equivalent form was formulated by Gy\'arf\'as: if the edges of a complete graph K are colored with ...
Gyárfás, András, Király, Zoltán
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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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Nearly Perfect Matchings in Uniform Hypergraphs
SIAM Journal on Discrete Mathematics, 2021 In this paper, we study degree conditions for the existence of large matchings in uniform hypergraphs. We prove that for integers $k,l,n$ with $k\ge 3$, $k/2{n-l\choose k-l}-{(n-l)-(\lceil n/k \rceil-2)\choose 2}$, then $H$ has a matching covering all but a constant number of vertices.
Lu, Hongliang +2 more
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The minimum vertex degree for an almost-spanning tight cycle in a $3$-uniform hypergraph [PDF]
, 2016 We prove that any $3$-uniform hypergraph whose minimum vertex degree is at least $\left(\frac{5}{9} + o(1) \right)\binom{n}{2}$ admits an almost-spanning tight cycle, that is, a tight cycle leaving $o(n)$ vertices uncovered.
Cooley, Oliver, Mycroft, Richard
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