Results 21 to 30 of about 2,959 (186)
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.
Zdenek Dvorák 0001 +3 more
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Learnable Hypergraph Laplacian for Hypergraph Learning
ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2022 HyperGraph Convolutional Neural Networks (HGCNNs) have demonstrated their potential in modeling high-order relations preserved in graph structured data. However, most existing convolution filters are localized and determined by the pre-defined initial hypergraph topology, neglecting to explore implicit and long-ange relations in real-world data.
Jiying Zhang +4 more
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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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Journal of the London Mathematical Society, 2019 Let $\text{Tr}(n,m,k)$ denote the largest number of distinct projections onto $k$ coordinates guaranteed in any family of $m$ binary vectors of length $n$. The classical Sauer-Perles-Shelah Lemma implies that $\text{Tr}(n, n^r, k) = 2^k$ for $k \le r$. While determining $\text{Tr}(n,n^r,k)$ precisely for general $k$ seems hopeless even for constant $r$,
Noga Alon, Guy Moshkovitz, Noam Solomon
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On partitioning of hypergraphs
Discrete Mathematics, 2007 The edge-isoperimetric problem on graphs (EIP), namely for a given integer \(m\) and graph \(G=(V,E)\) to find a subset \(A\) of the vertices of \(G\) of cardinality \(m\) so that the number of edges of \(G\) connecting vertices in \(A\) to vertices in \(V\setminus A\), is minimized (version 1), or such that the number of edges of \(G\) induced by \(A\)
S. Bezrukov, Battiti, Roberto
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On Matchings in Hypergraphs [PDF]
The Electronic Journal of Combinatorics, 2012 We show that if the largest matching in a $k$-uniform hypergraph $G$ on $n$ vertices has precisely $s$ edges, and $n>2k^2s/\log k$, then $H$ has at most $\binom n k - \binom {n-s} k $ edges and this upper bound is achieved only for hypergraphs in which the set of edges consists of all $k$-subsets which intersect a given set of $s$ vertices.
Peter Frankl +2 more
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Characterizing the hypergraph-of-entity and the structural impact of its extensions
Applied Network Science, 2020 The hypergraph-of-entity is a joint representation model for terms, entities and their relations, used as an indexing approach in entity-oriented search.
José Devezas, Sérgio Nunes
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Algebraic structures and lattice properties of hypergraph Pre-Rough sets [PDF]
Mathematics and Computational SciencesThe study introduces and examines the concept of hypergraph pre-rough sets, which are developed by combining minimum soft descriptions with hypergraph structures.
Ganesan Gomathi +3 more
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Almost Self-Complementary Uniform Hypergraphs
Discussiones Mathematicae Graph Theory, 2018 A k-uniform hypergraph (k-hypergraph) is almost self-complementary if it is isomorphic with its complement in the complete k-uniform hypergraph minus one edge. We prove that an almost self-complementary k-hypergraph of order n exists if and only if (nk)$\
Wojda Adam Paweł
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Individual Differences in Dynamic Functional Brain Connectivity across the Human Lifespan. [PDF]
PLoS Computational Biology, 2016 Individual differences in brain functional networks may be related to complex personal identifiers, including health, age, and ability. Dynamic network theory has been used to identify properties of dynamic brain function from fMRI data, but the majority
Elizabeth N Davison +6 more
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