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Sampling uniform hypergraphs with given degrees [PDF]
, 2022 Graphs are combinatorial objects commonly used to model relationships between pairs of entities. Hypergraphs are a generalization of graphs in which edges connect an arbitrary number of vertices.
Ross, James
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On the Degree Sequences of Uniform Hypergraphs [PDF]
, 2013 In hypergraph theory, determining a good characterization of d, the degree sequence of an h-uniform hypergraph $\mathcal{H}$, and deciding the complexity status of the reconstruction of $\mathcal{H}$ from d, are two challenging open problems. They can be formulated in the context of discrete tomography: asks whether there is a matrix A with nonnegative
FROSINI, ANDREA +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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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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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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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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Decompositions of Complete Uniform Multipartite Hypergraphs [PDF]
, 2020 In recent years, researchers have studied the existence of complete uniform hypergraphs into small-order hypergraphs. In particular, results on small 3-uniform graphs including loose 3, 4, and 5 cycles have been studied, as well as 4-uniform loose cycles
Ward, Patrick
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Saturated r-uniform hypergraphs
Discrete Mathematics, 1991 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Paul Erdös, Zoltán Füredi, Zsolt Tuza
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On upper transversals in 3-uniform hypergraphs [PDF]
, 2018 A set S of vertices in a hypergraph H is a transversal if it has a nonempty intersection with every edge of H. The upper transversal number Υ(H) of H is the maximum cardinality of a minimal transversal in H.
Yeo, Anders; id_orcid +1 more
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