This paper studies the problem of the spectral radius of the uniform hypergraph determined by the signless Laplacian matrix.The upper bound of the spectral radius of a uniform hypergraph is obtained by using Rayleigh ...This paper studies the problem of the spectral radius of the uniform hypergraph determined by the signless Laplacian matrix.The upper bound of the spectral radius of a uniform hypergraph is obtained by using Rayleigh principle and the perturbation of the spectral radius under moving the edge operation,and the extremal hypergraphs are characterized for both supertree and unicyclic hypergraphs.The spectral radius of the graph is generalized.展开更多
The problem of decomposing a complete 3-uniform hypergraph into Hamilton cycles was introduced by Bailey and Stevens using a generalization of Hamiltonian chain to uniform hypergraphs by Katona and Kierstead. Decompos...The problem of decomposing a complete 3-uniform hypergraph into Hamilton cycles was introduced by Bailey and Stevens using a generalization of Hamiltonian chain to uniform hypergraphs by Katona and Kierstead. Decomposing the complete 3-uniform hypergraphs Kn（3） into k-cycles （3 ≤ k 〈 n） was then considered by Meszka and Rosa. This study investigates this problem using a difference pattern of combinatorics and shows that Kn·5m（3） can be decomposed into 5-cycles for n ∈ {5, 7, 10, 11, 16, 17, 20, 22, 26} using computer programming.展开更多
It is proved in this paper that if G is a simple connected r-uniform hypergraph with ｜｜G｜｜≥2, then G has an edge e such that G - e - V1（e） is also a simple connected r-uniform hypergraph. This reduction is natu...It is proved in this paper that if G is a simple connected r-uniform hypergraph with ｜｜G｜｜≥2, then G has an edge e such that G - e - V1（e） is also a simple connected r-uniform hypergraph. This reduction is naturally called a combined Graham reduction. Under the simple reductions of single edge removals and single edge contractions, the minor minimal connected simple r-uniform hypergraphs are also determined.展开更多
Let F be a graph and H be a hypergraph.We say that H contains a Berge-F If there exists a bijectionψ:E(F)→E(H)such that for Ve E E(F),e C(e),and the Turan number of Berge-F is defined to be the maximum number of edg...Let F be a graph and H be a hypergraph.We say that H contains a Berge-F If there exists a bijectionψ:E(F)→E(H)such that for Ve E E(F),e C(e),and the Turan number of Berge-F is defined to be the maximum number of edges in an r-uniform hypergraph of order n that is Berge-F-free,denoted by ex,(n,Berge-F).A linear forest is a graph whose connected components are all paths or isolated vertices.Let Ln,k be the family of all linear forests of n vertices with k edges.In this paper,Turan number of Berge-Ln,in an r-uniform hypergraph is studied.When r≥k+1 and 3≤r≤l[]=1,we determine 2 the exact value of ex,(n,Berge-Ln,)respectively.When K-1≤r≤k,we 2 determine the upper bound of ex,(n,Berge-Ln,).展开更多
A hypergraph H is an(n,m)-hypergraph if it contains n vertices and m hyperedges,where n≥1 and m≥0 are two integers.Let k be a positive integer and let L be a set of nonnegative integers.A hyper graph H is k-uniform ...A hypergraph H is an(n,m)-hypergraph if it contains n vertices and m hyperedges,where n≥1 and m≥0 are two integers.Let k be a positive integer and let L be a set of nonnegative integers.A hyper graph H is k-uniform if all its hyperedges have the same size k,and H is L-intersecting if the number of common vertices of every two hyperedges belongs to L.In this paper,we propose and investigate the problem of estimating the maximum k among all k-uniform L-intersecting(n,m)-hypergraphs for fixed n,m and L.We will provide some tight upper and lower bounds on k in terms of n,m and L.展开更多
We employ graph parameter, the rupture degree, to measure the vulnerability of k-uniform hypergraph G<sup>k</sup>. For the k-uniform hypergraph G<sup>k</sup> underlying a non-complete graph G =...We employ graph parameter, the rupture degree, to measure the vulnerability of k-uniform hypergraph G<sup>k</sup>. For the k-uniform hypergraph G<sup>k</sup> underlying a non-complete graph G = (V, E), its rupture degree r(G<sup>k</sup>) is defined as r(G<sup>k</sup>) = max{ω(G<sup>k</sup> - X) - |X| - m(G<sup>k</sup> - X): X <span style="white-space:nowrap;">⊂ V(G<sup>k</sup>), ω(G<sup>k</sup> - X) > 1}, where X is a cut set (or destruction strategy) of G<sup>k</sup>, ω(G<sup>k</sup> - X) and m(G<sup>k</sup> - X) denote the number of components and the order of a largest component in G<sup>k</sup> - X, respectively. It is shown that this parameter can be used to measure the vulnerability of networks. In this paper, the rupture degrees of several specific classes of k-uniform hypergraph are determined.展开更多
单个较大非均匀超图聚类旨在将非均匀超图包含的节点划分为多个簇,使得同一簇内的节点更相似,而不同簇中的节点更不相似,具有广泛的应用场景。目前,最优的基于超图神经网络的非均匀超图聚类方法CIAH(co-cluster the interactions via at...单个较大非均匀超图聚类旨在将非均匀超图包含的节点划分为多个簇,使得同一簇内的节点更相似,而不同簇中的节点更不相似,具有广泛的应用场景。目前,最优的基于超图神经网络的非均匀超图聚类方法CIAH(co-cluster the interactions via attentive hypergraph neural network)虽然较好地学习了非均匀超图的关系信息,但仍存在两点不足:(1)对于局部关系信息的挖掘不足;(2)忽略了隐藏的高阶关系。因此,提出一种基于多尺度注意力和动态超图构建的非均匀超图聚类模型MADC(non-uniform hypergraph clustering combining multi-scale attention and dynamic construction)。一方面,使用多尺度注意力充分学习了超边中节点与节点之间的局部关系信息;另一方面,采用动态构建挖掘隐藏的高阶关系,进一步丰富了超图特征嵌入。真实数据集上的大量实验结果验证了MADC模型在非均匀超图聚类上的聚类准确率(accuracy,ACC)、标准互信息(normalized mutual information,NMI)和调整兰德指数(adjusted Rand index,ARI)均优于CIAH等所有Baseline方法。展开更多
In this paper, we set ρ_r =~r4^（1/2） and ρ′_r= β^（-1/r）, where β =-1/6 ·（100 ＋ 12·（69）^（1/2））^（1/3）-2/（3·（100＋12·（69）^（1/2）））^（1/3）＋4/3≈0.2451223338. We consider conn...In this paper, we set ρ_r =~r4^（1/2） and ρ′_r= β^（-1/r）, where β =-1/6 ·（100 ＋ 12·（69）^（1/2））^（1/3）-2/（3·（100＋12·（69）^（1/2）））^（1/3）＋4/3≈0.2451223338. We consider connected r-uniform hypergraphs with spectral radius between ρ_r and ρ′_r and give a description of such hypergraphs.展开更多
In this paper, we consider the r-uniform hypergraphs H with spectral radius at most ■. We show that H must have a quipus-structure, which is similar to the graphs with spectral radius at most ■ [Woo-Neumaier, Graphs...In this paper, we consider the r-uniform hypergraphs H with spectral radius at most ■. We show that H must have a quipus-structure, which is similar to the graphs with spectral radius at most ■ [Woo-Neumaier, Graphs Combin. 2007].展开更多
基金Supported by Natural Science Foundation of HuBei Province(2022CFB299).
文摘This paper studies the problem of the spectral radius of the uniform hypergraph determined by the signless Laplacian matrix.The upper bound of the spectral radius of a uniform hypergraph is obtained by using Rayleigh principle and the perturbation of the spectral radius under moving the edge operation,and the extremal hypergraphs are characterized for both supertree and unicyclic hypergraphs.The spectral radius of the graph is generalized.
基金Supported by the National Natural Science Foundation of China(Grant No.11161032)
文摘The problem of decomposing a complete 3-uniform hypergraph into Hamilton cycles was introduced by Bailey and Stevens using a generalization of Hamiltonian chain to uniform hypergraphs by Katona and Kierstead. Decomposing the complete 3-uniform hypergraphs Kn（3） into k-cycles （3 ≤ k 〈 n） was then considered by Meszka and Rosa. This study investigates this problem using a difference pattern of combinatorics and shows that Kn·5m（3） can be decomposed into 5-cycles for n ∈ {5, 7, 10, 11, 16, 17, 20, 22, 26} using computer programming.
基金Supported by NRF South Africathe National Natural Science Foundation of China(Grant No.11161032)
文摘It is proved in this paper that if G is a simple connected r-uniform hypergraph with ｜｜G｜｜≥2, then G has an edge e such that G - e - V1（e） is also a simple connected r-uniform hypergraph. This reduction is naturally called a combined Graham reduction. Under the simple reductions of single edge removals and single edge contractions, the minor minimal connected simple r-uniform hypergraphs are also determined.
文摘Let F be a graph and H be a hypergraph.We say that H contains a Berge-F If there exists a bijectionψ:E(F)→E(H)such that for Ve E E(F),e C(e),and the Turan number of Berge-F is defined to be the maximum number of edges in an r-uniform hypergraph of order n that is Berge-F-free,denoted by ex,(n,Berge-F).A linear forest is a graph whose connected components are all paths or isolated vertices.Let Ln,k be the family of all linear forests of n vertices with k edges.In this paper,Turan number of Berge-Ln,in an r-uniform hypergraph is studied.When r≥k+1 and 3≤r≤l[]=1,we determine 2 the exact value of ex,(n,Berge-Ln,)respectively.When K-1≤r≤k,we 2 determine the upper bound of ex,(n,Berge-Ln,).
基金The authors would like to thank the referees for several remarks and suggestions. This work was supported in part by the Joint NSFC-ISF Research Program （jointly funded by the National Natural Science Foundation of China and the Israel Science Foundation （Grant No. 11561141001））, the National Natural Science Foundation of China （Grant Nos. 11531001 and 11271256）, Innovation Program of Shanghai Municipal Education Commission （Grant No. 14ZZ016） and SpeciMized Research Fund for the Doctoral Program of Higher Education （Grant No. 20130073110075）.
文摘We present several upper bounds for the adjacency and signless Laplacian spectral radii of uniform hypergraphs in terms of degree sequences.
基金Supported by National Natural Science Foundation of China(Grant Nos.12242111,12131013,12171393,12071370,71973103,U1803263,11601430)Natural Science Foundation of Shaanxi Province(Grant Nos.2021JM-040,2020JQ-099)+2 种基金Shaanxi Fundamental Science Research Project for Mathematics and Physics(Grant No.22JSZ009)Guangdong Basic and Applied Basic Research Foundation(Grant Nos.2023A1515030208,2022A1515010899)the Fundamental Research Funds for the Central Universities。
文摘A hypergraph H is an(n,m)-hypergraph if it contains n vertices and m hyperedges,where n≥1 and m≥0 are two integers.Let k be a positive integer and let L be a set of nonnegative integers.A hyper graph H is k-uniform if all its hyperedges have the same size k,and H is L-intersecting if the number of common vertices of every two hyperedges belongs to L.In this paper,we propose and investigate the problem of estimating the maximum k among all k-uniform L-intersecting(n,m)-hypergraphs for fixed n,m and L.We will provide some tight upper and lower bounds on k in terms of n,m and L.
文摘We employ graph parameter, the rupture degree, to measure the vulnerability of k-uniform hypergraph G<sup>k</sup>. For the k-uniform hypergraph G<sup>k</sup> underlying a non-complete graph G = (V, E), its rupture degree r(G<sup>k</sup>) is defined as r(G<sup>k</sup>) = max{ω(G<sup>k</sup> - X) - |X| - m(G<sup>k</sup> - X): X <span style="white-space:nowrap;">⊂ V(G<sup>k</sup>), ω(G<sup>k</sup> - X) > 1}, where X is a cut set (or destruction strategy) of G<sup>k</sup>, ω(G<sup>k</sup> - X) and m(G<sup>k</sup> - X) denote the number of components and the order of a largest component in G<sup>k</sup> - X, respectively. It is shown that this parameter can be used to measure the vulnerability of networks. In this paper, the rupture degrees of several specific classes of k-uniform hypergraph are determined.
基金Supported by the National Natural Science Foundation of China(Grant Nos.116013681140143411771322)
文摘In this paper, we set ρ_r =~r4^（1/2） and ρ′_r= β^（-1/r）, where β =-1/6 ·（100 ＋ 12·（69）^（1/2））^（1/3）-2/（3·（100＋12·（69）^（1/2）））^（1/3）＋4/3≈0.2451223338. We consider connected r-uniform hypergraphs with spectral radius between ρ_r and ρ′_r and give a description of such hypergraphs.
基金Supported by the National Natural Science Foundation of China(Grant No.11601368)
文摘In this paper, we consider the r-uniform hypergraphs H with spectral radius at most ■. We show that H must have a quipus-structure, which is similar to the graphs with spectral radius at most ■ [Woo-Neumaier, Graphs Combin. 2007].
