Results 11 to 20 of about 40,185 (227)
On the spectrum of hypergraphs
Linear Algebra and its Applications, 2016 Here we study the spectral properties of an underlying weighted graph of a non-uniform hypergraph by introducing different connectivity matrices, such as adjacency, Laplacian and normalized Laplacian matrices. We show that different structural properties
Chris Ritchie (1952305) +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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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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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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Quasirandomness in hypergraphs [PDF]
Electronic Notes in Discrete Mathematics, 2017 An $n$-vertex graph $G$ of edge density $p$ is considered to be quasirandom if it shares several important properties with the random graph $G(n,p)$. A well-known theorem of Chung, Graham and Wilson states that many such `typical' properties are asymptotically equivalent and, thus, a graph $G$ possessing one such property automatically satisfies the ...
Aigner-Horev, E +4 more
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Discrete Mathematics, 1985 Threshold graphs were introduced by \textit{V. Chvátal} and \textit{P. L. Hammer} [Ann. Discrete Math. 1, 145-162 (1977; Zbl 0384.90091)]. They gave three equivalent characterizations of these graphs. These characterizations were generalized for hypergraphs by \textit{M. Ch. Golumbic} [Combinatorics, Keszthely 1976, Colloq. Math.
Jan Reiterman +3 more
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, 2021 In this paper, we prove that for any $k\ge 3$, there exist infinitely many minimal asymmetric $k$-uniform hypergraphs. This is in a striking contrast to $k=2$, where it has been proved recently that there are exactly $18$ minimal asymmetric graphs. We also determine, for every $k\ge 1$, the minimum size of an asymmetric $k$-uniform hypergraph.
Yiting Jiang +2 more
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Intersections of hypergraphs [PDF]
Journal of Combinatorial Theory, Series B, 2015 Given two weighted k-uniform hypergraphs G, H of order n, how much (or little) can we make them overlap by placing them on the same vertex set? If we place them at random, how concentrated is the distribution of the intersection? The aim of this paper is to investigate these questions.
Bollobas, B, Scott, A
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ISPRS International Journal of Geo-Information, 2016 Spatial data processing often requires massive datasets, and the task/data scheduling efficiency of these applications has an impact on the overall processing performance.
Bo Cheng, Xuefeng Guan, Huayi Wu, Rui Li
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Even order uniform hypergraph via the Einstein product
AKCE International Journal of Graphs and Combinatorics, 2023 We propose the algebraic connectivity of an undirected 2m-uniform hypergraph under the Einstein product. We generalize the algebraic connectivity to a directed 2m-uniform hypergraph and reveal the relationship between the vertex connectivity and the ...
Jiaqi Gu, Yimin Wei
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