Results 11 to 20 of about 1,354,678 (274)
On the α-Spectral Radius of Uniform Hypergraphs
Discussiones Mathematicae Graph Theory, 2020 For 0 ≤ α ---lt--- 1 and a uniform hypergraph G, the α-spectral radius of G is the largest H-eigenvalue of αD(G)+(1−α)A(G), where D(G) and A(G) are the diagonal tensor of degrees and the adjacency tensor of G, respectively. We give upper bounds for the α-
Guo Haiyan, Zhou Bo
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Discrete Mathematics, 1986 AbstractGiven two integers π > 0 and β ⩾ 0, we prove that there exists a finite k-uniform hypergraph (resp. a finite connected k-uniform hpergraph) whose automorphism group has exactly π point orbits and β block orbits if and only if π⩽ κβ + 1 (resp. π ⩽ (κ − 1) β + 1).
Anne Delandtsheer
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On Lagrangians of r-uniform hypergraphs [PDF]
Journal of Combinatorial Optimization, 2013 A remarkable connection between the order of a maximum clique and the Lagrangian of a graph was established by Motzkin and Straus in [7]. This connection and its extensions were successfully employed in optimization to provide heuristics for the maximum clique number in graphs. It has been also applied in spectral graph theory.
Yuejian Peng, Qingsong Tang, Cheng Zhao
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Matchings in 3-uniform hypergraphs
Journal of Combinatorial Theory, Series B, 2010 We determine the minimum vertex degree that ensures a perfect matching in a 3-uniform hypergraph. More precisely, suppose that H is a sufficiently large 3-uniform hypergraph whose order n is divisible by 3. If the minimum vertex degree of H is greater than \binom{n-1}{2}-\binom{2n/3}{2}, then H contains a perfect matching.
Daniela Kühn +2 more
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Partial recovery and weak consistency in the non-uniform hypergraph stochastic block model [PDF]
Combinatorics, probability & computing, 2021 We consider the community detection problem in sparse random hypergraphs under the non-uniform hypergraph stochastic block model (HSBM), a general model of random networks with community structure and higher-order interactions.
Ioana Dumitriu, Haixiao Wang, Yizhe Zhu
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The existence of bipartite almost self-complementary 3-uniform hypergraphs [PDF]
Opuscula Mathematica, 2023 An almost self-complementary 3-uniform hypergraph on \(n\) vertices exists if and only if \(n\) is congruent to 3 modulo 4 A hypergraph \(H\) with vertex set \(V\) and edge set \(E\) is called bipartite if \(V\) can be partitioned into two subsets \(V_1\
L.N. Kamble +2 more
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Judicious partitions of uniform hypergraphs [PDF]
Combinatorica, 2014 The vertices of any graph with $m$ edges may be partitioned into two parts so that each part meets at least $\frac{2m}{3}$ edges. Bollob s and Thomason conjectured that the vertices of any $r$-uniform hypergraph with $m$ edges may likewise be partitioned into $r$ classes such that each part meets at least $\frac{r}{2r-1}m$ edges.
John Haslegrave
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A Cheeger Cut for Uniform Hypergraphs [PDF]
Graphs and Combinatorics, 2021 AbstractThe graph Cheeger constant and Cheeger inequalities are generalized to the case of hypergraphs whose edges have the same cardinality. In particular, it is shown that the second largest eigenvalue of the generalized normalized Laplacian is bounded both above and below by the generalized Cheeger constant, and the corresponding eigenfunctions can ...
Raffaella Mulas, Raffaella Mulas
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The Laplacian of a uniform hypergraph
Journal of Combinatorial Optimization, 2015 In this paper, we investigate the Laplacian, i.e., the normalized Laplacian tensor of a $$k$$ -uniform hypergraph. We show that the real parts of all the eigenvalues of the Laplacian are in the interval $$[0,2]$$ , and the real part is zero (respectively two) if and only if the eigenvalue is zero (respectively two). All the H $$^+$$ -eigenvalues of the
Shenglong Hu, L. Qi
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Super edge-magic labeling for 𝒌-uniform, complete 𝒌-uniform and complete 𝒌-uniform 𝒌-partite hypergraphs [PDF]
Songklanakarin Journal of Science and Technology (SJST), 2021 Let 𝐻 be a hypergraph with a vertex set 𝑉 and a hyperedge set 𝐸. Generalized from the super edge-magic in a graph, we say that a hypergraph 𝐻 is super edge-magic if there is a bijection 𝑓: 𝑉 ∪ 𝐸 → {1,2,3, … , |𝑉| + |𝐸|} which satisfies: (i) there exists
Ratinan Boonklurb +2 more
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