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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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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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The characteristic polynomials of uniform double hyperstars and uniform hypertriangles [PDF]
, 2023 A k-power hypergraph is obtained from a graph by adding k−2 new vertices to each edge of the graph. A k-uniform double hyperstar is the k-power hypergraph of a double star. The k-uniform hypertriangle is the k-power hypergraph of a triangle.
Edwin R. van Dam +5 more
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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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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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On $\alpha$-spectral theory of a directed k-uniform hypergraph [PDF]
Computer Science Journal of Moldova, 2020 In this paper, we study a k-uniform directed hypergraph in general form and introduce its adjacency tensor, Laplacian tensor and signless Laplacian tensor. For the $k$-uniform directed hypergraph $\mathcal{H}$ and $0\leq \alpha
Gholam-Hasan Shirdel +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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Diagonal Forms, Linear Algebraic Methods and Ramsey-Type Problems [PDF]
, 2013 This thesis focuses mainly on linear algebraic aspects of combinatorics. Let N_t(H) be an incidence matrix with edges versus all subhypergraphs of a complete hypergraph that are isomorphic to H. Richard M.
Wong, Wing Hong Tony
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Hypergraph partitioning using tensor eigenvalue decomposition.
PLoS ONE, 2023 Hypergraphs have gained increasing attention in the machine learning community lately due to their superiority over graphs in capturing super-dyadic interactions among entities.
Deepak Maurya, Balaraman Ravindran
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