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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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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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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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-partite self-complementary and almost self-complementary -uniform hypergraphs
AKCE International Journal of Graphs and Combinatorics, 2020 A hypergraph is said to be -partite -uniform if its vertex set can be partitioned into non-empty sets so that every edge in the edge set , consists of precisely one vertex from each set , . It is denoted as or if for .
L.N. Kamble +2 more
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On hamiltonian chain saturated uniform hypergraphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 Graphs and ...
Aneta Dudek, Andrzej Zak
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Dense Peelable Random Uniform Hypergraphs [PDF]
, 2019 We describe a new family of k-uniform hypergraphs with independent random edges. The hypergraphs have a high probability of being peelable, i.e. to admit no sub-hypergraph of minimum degree 2, even when the edge density (number of edges over vertices) is
Dietzfelbinger, Martin, Walzer, Stefan
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Matchings and Hamilton cycles in hypergraphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 It is well known that every bipartite graph with vertex classes of size $n$ whose minimum degree is at least $n/2$ contains a perfect matching. We prove an analogue of this result for uniform hypergraphs. We also provide an analogue of Dirac's theorem on
Daniela Kühn, Deryk Osthus
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Hamiltonian decompositions of complete k-uniform hypergraphs [PDF]
, 2010 Using a generalisation of Hamiltonian cycles to uniform hypergraphs due to Katona and Kierstead, we define a new notion of a Hamiltonian decomposition of a uniform hypergraph.
Bailey, Robert F., Stevens, Brett
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