Results 1 to 10 of about 1,548 (146)
Decomposing hypergraphs into k-colorable hypergraphs [PDF]
Transactions on Combinatorics, 2014 For a given hypergraph $H$ with chromatic number $chi(H)$ and with no edge containing only one vertex, it is shown that the minimum number $l$ for which there exists a partition (also a covering) ${E_1,E_2,ldots,E_l}$ for $E(H)$, such that the ...
Gholamreza Omidi , Khosro Tajbakhsh
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Discussiones Mathematicae Graph Theory, 2016 If D = (V,A) is a digraph, its niche hypergraph NH(D) = (V, E) has the edge set ℇ = {e ⊆ V | |e| ≥ 2 ∧ ∃ v ∈ V : e = N−D(v) ∨ e = N+D(v)}. Niche hypergraphs generalize the well-known niche graphs (see [11]) and are closely related to competition ...
Garske Christian +2 more
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Hypergraph Based Berge Hypergraphs [PDF]
Graphs and Combinatorics, 2021 Fix a hypergraph $\mathcal{F}$. A hypergraph $\mathcal{H}$ is called a {\it Berge copy of $\mathcal{F}$} or {\it Berge-$\mathcal{F}$} if we can choose a subset of each hyperedge of $\mathcal{H}$ to obtain a copy of $\mathcal{F}$. A hypergraph $\mathcal{H}$ is {\it Berge-$\mathcal{F}$-free} if it does not contain a subhypergraph which is Berge copy of $\
Balko, Martin +4 more
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Hypergraph convolution and hypergraph attention [PDF]
Pattern Recognition, 2021 Recently, graph neural networks have attracted great attention and achieved prominent performance in various research fields. Most of those algorithms have assumed pairwise relationships of objects of interest. However, in many real applications, the relationships between objects are in higher-order, beyond a pairwise formulation.
Song Bai, Feihu Zhang, Philip H.S. Torr
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Heliyon, 2022 Topological invariants are numerical parameters of graphs or hypergraphs that indicate its topology and are known as graph or hypergraph invariants. In this paper, topological indices of hypergraphs such as Wiener index, degree distance index and Gutman ...
Sakina Ashraf +3 more
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Hypergraph and Uncertain Hypergraph Representation Learning Theory and Methods
Mathematics, 2022 With the advent of big data and the information age, the data magnitude of various complex networks is growing rapidly. Many real-life situations cannot be portrayed by ordinary networks, while hypergraphs have the ability to describe and characterize ...
Liyan Zhang +5 more
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Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2023 Complexity science provides a powerful framework for understanding physical, biological and social systems, and network analysis is one of its principal tools. Since many complex systems exhibit multilateral interactions that change over time, in recent years, network scientists have become increasingly interested in modelling and ...
Corinna Coupette +2 more
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Journal of Combinatorial Theory, Series B, 2021 The following very natural problem was raised by Chung and Erd s in the early 80's and has since been repeated a number of times. What is the minimum of the Tur n number $\text{ex}(n,\mathcal{H})$ among all $r$-graphs $\mathcal{H}$ with a fixed number of edges?
Matija Bucić +3 more
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Sharp Bounds on the Spectral Radii of Uniform Hypergraphs concerning Diameter or Clique Number
Discrete Dynamics in Nature and Society, 2021 In this paper, we defined two classes of hypergraphs, hyperbugs and kite hypergraphs. We show that balanced hyperbugs maximize the spectral radii of hypergraphs with fixed number of vertices and diameter and kite hypergraphs minimize the spectral radii ...
Qiannan Niu, Haizhen Ren, Lei Zhang
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On Clustering Detection Based on a Quadratic Program in Hypergraphs
Journal of Mathematics, 2022 A proper cluster is usually defined as maximally coherent groups from a set of objects using pairwise or more complicated similarities. In general hypergraphs, clustering problem refers to extraction of subhypergraphs with a higher internal density, for ...
Qingsong Tang
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