Results 91 to 100 of about 11,526 (190)
Constrained Colouring and σ-Hypergraphs
Discussiones Mathematicae Graph Theory, 2015 A constrained colouring or, more specifically, an (α, β)-colouring of a hypergraph H, is an assignment of colours to its vertices such that no edge of H contains less than α or more than β vertices with different colours.
Caro Yair, Lauri Josef, Zarb Christina
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Randomized Hypergraph States and Their Entanglement Properties
Annalen der Physik, Volume 538, Issue 1, January 2026.Randomized hypergraph (RH) states are mixed states that extend the concept of randomized graph states to multi‐qubit hypergraphs subject to probabilistic gate imperfections. By modeling noisy multi‐qubit operations, this work reveals nonmonotonic behavior in bipartite and multipartite entanglement, derives analytical witnesses for specific hypergraph ...
Vinícius Salem +2 more
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Steiner Triple Systems With High Discrepancy
Journal of Combinatorial Designs, Volume 34, Issue 1, Page 5-14, January 2026.ABSTRACT In this paper, we initiate the study of discrepancy questions for combinatorial designs. Specifically, we show that, for every fixed r ≥ 3 and n ≡ 1 , 3 ( mod 6 ), any r‐colouring of the triples on [ n ] admits a Steiner triple system of order n with discrepancy Ω ( n 2 ).
Lior Gishboliner +2 more
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A note on self-complementary 4-uniform hypergraphs [PDF]
Opuscula Mathematica, 2005 We prove that a permutation \(\theta\) is complementing permutation for a \(4\)-uniform hypergraph if and only if one of the following cases is satisfied: (i) the length of every cycle of \(\theta\) is a multiple of \(8\), (ii) \(\theta\) has \(1\), \(2\)
Artur Szymański
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Cycle decompositions in k-uniform hypergraphs
Journal of Combinatorial Theory, Series Bv3: including referee comments.
Allan Lo +2 more
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Hypergraphs with Pendant Paths are not Chromatically Unique
Discussiones Mathematicae Graph Theory, 2014 In this note it is shown that every hypergraph containing a pendant path of length at least 2 is not chromatically unique. The same conclusion holds for h-uniform r-quasi linear 3-cycle if r ≥ 2.
Tomescu Ioan
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Hypergraph Representation via Axis-Aligned Point-Subspace Cover [PDF]
Discrete Mathematics & Theoretical Computer ScienceWe propose a new representation of $k$-partite, $k$-uniform hypergraphs, that is, a hypergraph with a partition of vertices into $k$ parts such that each hyperedge contains exactly one vertex of each type; we call them $k$-hypergraphs for short.
Oksana Firman, Joachim Spoerhase
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Small cores in 3-uniform hypergraphs
Journal of Combinatorial Theory, Series B, 2017 The main result of this paper is that for any $c>0$ and for large enough $n$ if the number of edges in a 3-uniform hypergraph is at least $cn^2$ then there is a core (subgraph with minimum degree at least 2) on at most 15 vertices. We conjecture that our result is not sharp and 15 can be replaced by 9.
David Solymosi, Jozsef Solymosi
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Equitable Coloring ofk-Uniform Hypergraphs [PDF]
SIAM Journal on Discrete Mathematics, 2003 Let $H$ be a $k$-uniform hypergraph with $n$ vertices. A {\em strong $r$-coloring} is a partition of the vertices into $r$ parts, such that each edge of $H$ intersects each part. A strong $r$-coloring is called {\em equitable} if the size of each part is $\lceil n/r \rceil$ or $\lfloor n/r \rfloor$.
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Wickets in 3-uniform hypergraphs
Discrete MathematicsIn these notes, we consider a Turán-type problem in hypergraphs. What is the maximum number of edges if we forbid a subgraph? Let $H_n^{(3)}$ be a 3-uniform linear hypergraph, i.e. any two edges have at most one vertex common. A special hypergraph, called {\em wicket}, is formed by three rows and two columns of a $3 \times 3$ point matrix.
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