5 papers
A two-steps tensor eigenvector centrality for nodes and hyperedges in hypergraphs
Qing Xu, Chunmeng Liu, Changjiang Bu +1
Hypergraphs have been a powerful tool to represent higher-order interactions, where hyperedges can connect an arbitrary number of nodes. Quantifying the relative importance of node…
The -core of a graph and its high-order spectra
Chunmeng Liu, Qing Xu, Changjiang Bu
The -core of a graph is its largest subgraph with minimum degree at least , a fundamental concept for uncovering hierarchical structures. In this paper, we establish a connec…
Bollobás-Nikiforov conjecture holds asymptotically almost surely
Chunmeng Liu, Changjiang Bu
Bollobás and Nikiforov (J. Combin. Theory Ser. B. 97 (2007) 859-865) conjectured that for a graph with edges and the clique number , then $ λ_{1}^{2}+λ_{2}^{2}\leq…
A tensor's spectral bound on the clique number
Chunmeng Liu, Changjiang Bu
In this paper, we study the spectral radius of the clique tensor A(G) associated with a graph G. This tensor is a higher-order extensions of the adjacency matrix of G. A lower boun…
An Erdős-Stone type result for high-order spectra of graphs
Chunmeng Liu, Jiang Zhou, Changjiang Bu
Erdős-Stone Theorem is a well-known result in extremal graph theory which determines the asymptotic behaviour of maximum number of edges in an -vertex -free graph. In 2009, N…