Results 131 to 140 of about 1,354,678 (274)
AI Magazine, Volume 46, Issue 1, Spring 2025.Abstract A cornerstone of machine learning is the identification and exploitation of structure in high‐dimensional data. While classical approaches assume that data lies in a high‐dimensional Euclidean space, geometric machine learning methods are designed for non‐Euclidean data, including graphs, strings, and matrices, or data characterized by ...
Melanie Weber
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A Measure for the Vulnerability of Uniform Hypergraph Networks: Scattering Number
MathematicsThe scattering number of a graph G is defined as s(G)=max{ω(G−X)−|X|:X⊂V(G),ω(G−X)>1}, where X is a cut set of G, and ω(G−X) denotes the number of components in G−X, which can be used to measure the vulnerability of network G.
Ning Zhao, Haixing Zhao, Yinkui Li
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Small cores in 3-uniform hypergraphs
Journal of Combinatorial Theory, Series B, 2017 The main result of this paper is that for any $c>0$ and for large enough $n$ if the number of edges in a 3-uniform hypergraph is at least $cn^2$ then there is a core (subgraph with minimum degree at least 2) on at most 15 vertices. We conjecture that our result is not sharp and 15 can be replaced by 9.
David Solymosi, Jozsef Solymosi
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A Note on the Local Observability of Uniform Hypergraphs
PAMM, Volume 25, Issue 1, March 2025.ABSTRACT Hypergraphs generalize graphs in such a way that edges may connect any number of nodes. If all edges are adjacent to the same number of nodes, the hypergraph is called uniform. Thus, a graph is a 2‐uniform hypergraph. Each uniform hypergraph can be identified with an autonomous dynamical state‐space system, whose vector field is composed of ...
Daniel Gerbet, Klaus Röbenack
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Perfect Matchings and Loose Hamilton Cycles in the Semirandom Hypergraph Model
Random Structures &Algorithms, Volume 66, Issue 2, March 2025.ABSTRACT We study the 2‐offer semirandom 3‐uniform hypergraph model on n$$ n $$ vertices. At each step, we are presented with 2 uniformly random vertices. We choose any other vertex, thus creating a hyperedge of size 3. We show a strategy that constructs a perfect matching and another that constructs a loose Hamilton cycle, both succeeding ...
Michael Molloy +2 more
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On vertex independence number of uniform hypergraphs
Acta Universitatis Sapientiae: Informatica, 2014 Let H be an r-uniform hypergraph with r ≥ 2 and let α(H) be its vertex independence number. In the paper bounds of α(H) are given for different uniform hypergraphs: if H has no isolated vertex, then in terms of the degrees, and for triangle-free linear H
Chishti Tariq A. +3 more
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A note on self-complementary 4-uniform hypergraphs [PDF]
Opuscula Mathematica, 2005 We prove that a permutation \(\theta\) is complementing permutation for a \(4\)-uniform hypergraph if and only if one of the following cases is satisfied: (i) the length of every cycle of \(\theta\) is a multiple of \(8\), (ii) \(\theta\) has \(1\), \(2\)
Artur Szymański
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Constrained Colouring and σ-Hypergraphs
Discussiones Mathematicae Graph Theory, 2015 A constrained colouring or, more specifically, an (α, β)-colouring of a hypergraph H, is an assignment of colours to its vertices such that no edge of H contains less than α or more than β vertices with different colours.
Caro Yair, Lauri Josef, Zarb Christina
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Existential closure in uniform hypergraphs
Discrete MathematicsFor a positive integer $n$, a graph with at least $n$ vertices is $n$-existentially closed or simply $n$-e.c. if for any set of vertices $S$ of size $n$ and any set $T\subseteq S$, there is a vertex $x\not\in S$ adjacent to each vertex of $T$ and no vertex of $S\setminus T$.
Andrea C. Burgess +2 more
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Hypergraphs with Pendant Paths are not Chromatically Unique
Discussiones Mathematicae Graph Theory, 2014 In this note it is shown that every hypergraph containing a pendant path of length at least 2 is not chromatically unique. The same conclusion holds for h-uniform r-quasi linear 3-cycle if r ≥ 2.
Tomescu Ioan
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