Results 11 to 20 of about 41,298 (230)
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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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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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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Contributions to Discrete Mathematics, 2023 This article presents an extension of the study of metric and partition dimension to hypergraphs. We give sharp lower bounds for the metric and partition dimension of hypergraphs in general and give exact values under specified conditions.
Imran Javaid +3 more
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Trends in Biotechnology, 2014 Signaling pathways function as the information-passing mechanisms of cells. A number of databases with extensive manual curation represent the current knowledge base for signaling pathways. These databases motivate the development of computational approaches for prediction and analysis.
Anna, Ritz +4 more
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The k-annihilating-ideal hypergraph of commutative ring
AKCE International Journal of Graphs and Combinatorics, 2019 The concept of the annihilating-ideal graph of a commutative ring was introduced by Behboodi et. al in 2011. In this paper, we extend this concept to the hypergraph for which we define an algebraic structure called k-annihilating-ideal of a commutative ...
K. Selvakumar, V. Ramanathan
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Nonintersecting Ryser Hypergraphs [PDF]
SIAM Journal on Discrete Mathematics, 2020 8 pages, some corrections in the proof of Lemma 3.6, added more explanation in the appendix, and other minor ...
Bishnoi A., Pepe V.
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Multi-order hypergraph convolutional networks integrated with self-supervised learning
Complex & Intelligent Systems, 2023 Hypergraphs, as a powerful representation of information, effectively and naturally depict complex and non-pair-wise relationships in the real world. Hypergraph representation learning is useful for exploring complex relationships implicit in hypergraphs.
Jiahao Huang +5 more
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The Electronic Journal of Combinatorics, 2010 The notion of pattern hypergraph provides a unified view of several previously studied coloring concepts. A pattern hypergraph $H$ is a hypergraph where each edge is assigned a type $\Pi_i$ that determines which of possible colorings of the edge are proper. A vertex coloring of $H$ is proper if it is proper for every edge.
Dvořák, Zdeněk +3 more
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