Results 91 to 100 of about 41,298 (230)
Information-Theoretic Limits and Strong Consistency on Binary Non-uniform Hypergraph Stochastic Block Models [PDF]
, 2023 Hai‐Xiao Wang
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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.
Jiang, Yiting, Nešetřil, Jaroslav
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Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract In 1935, Philip Hall published what is often referred to as ‘Hall's marriage theorem’ in a short paper (P. Hall, J. Lond. Math. Soc. (1) 10 (1935), no. 1, 26–30.) This paper has been very influential. I state the theorem and outline Hall's proof, together with some equivalent (or stronger) earlier results, and proceed to discuss some the many ...
Peter J. Cameron
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Beyond pairwise clustering [PDF]
, 2005 We consider the problem of clustering in domains where the affinity relations are not dyadic (pairwise), but rather triadic, tetradic or higher. The problem is an instance of the hypergraph partitioning problem.
Agarwal, Sameer +5 more
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Colorful Subhypergraphs in Kneser Hypergraphs [PDF]
The Electronic Journal of Combinatorics, 2014 Using a $\mathbb{Z}_q$-generalization of a theorem of Ky Fan, we extend to Kneser hypergraphs a theorem of Simonyi and Tardos that ensures the existence of multicolored complete bipartite graphs in any proper coloring of a Kneser graph. It allows to derive a lower bound for the local chromatic number of Kneser hypergraphs (using a natural definition of
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CoRoFR: Community Detection of Feature Graph Improves Feature Selection Using Robust Fuzzy Rough Set
Advanced Intelligent Systems, Volume 7, Issue 12, December 2025.In machine learning, features often function as communities in many tasks, especially in medicine. However, existing feature selection methods struggle to mine feature collaborations, which can boost predictive performance. Moreover, they are noise‐sensitive, leading to suboptimal feature selection and accuracy degradation.
Duanyang Feng +4 more
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Minimum-Weight Edge Discriminator in Hypergraphs [PDF]
, 2012 In this paper we introduce the concept of minimum-weight edge-discriminators in hypergraphs, and study its various properties. For a hypergraph $\mathcal H=(\mathcal V, \mathcal E)$, a function $\lambda: \mathcal V\rightarrow \mathbb Z^{+}\cup\{0\}$ is ...
Bhattacharya, Bhaswar B. +2 more
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Multi-omics data integration analysis of prostate cancer based on sparse least partial squares regression algorithm based on hypergraph regularization [PDF]
, 2023 Ruohui Huang +8 more
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Journal of Combinatorial Designs, Volume 33, Issue 12, Page 456-470, December 2025.ABSTRACT A family ℱ of subsets of [ n ] = { 1 , 2 , … , n } shatters a set A ⊆ [ n ] if for every A ′ ⊆ A, there is an F ∈ ℱ such that F ∩ A = A '. We develop a framework to analyze f ( n , k , d ), the maximum possible number of subsets of [ n ] of size d that can be shattered by a family of size k.
Noga Alon +2 more
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The Turán problem for hypergraphs of fixed size [PDF]
, 2005 We obtain a general bound on the Turán density of a hypergraph in terms of the number of edges that it contains. If F is an r-uniform hypergraph with f edges we show that [pi](F) =3 and f->[infinity]
Keevash, Peter
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