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math.CO2025
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…
math.CO2025
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…