The smallest eigenvalue of \(K_{r}\)-free graphs

DOI10.1016/j.disc.2006.01.014zbMath1089.05049arXivmath/0410216OpenAlexW2000285611MaRDI QIDQ2488937

Vladimir Nikiforov

Publication date: 16 May 2006

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0410216

zbMATH Keywords

Independence numberGraph eigenvalueSecond eigenvalueSmallest eigenvalue

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69)

Related Items (13)

Eigenvalues and forbidden subgraphs. I. ⋮ Connected \((K_4 - e)\)-free graphs whose second largest eigenvalue does not exceed 1 ⋮ New results for MaxCut in H$H$‐free graphs ⋮ Bounds for A_α-eigenvalues ⋮ The minimum spectral radius of \(K_{r + 1}\)-saturated graphs ⋮ Dimension-free bounds and structural results in communication complexity ⋮ Graphs for which the least eigenvalue is minimal. I ⋮ The least eigenvalue of a graph with a given domination number ⋮ A simpler characterization of a spectral lower bound on the clique number ⋮ The maximum spectral radius of \(C_4\)-free graphs of given order and size ⋮ More spectral bounds on the clique and independence numbers ⋮ A sharp lower bound for the spectral radius in \(K_4\)-saturated graphs ⋮ Unnamed Item

Cites Work

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• Triangle factors in sparse pseudo-random graphs
• Graphs and Hermitian matrices: eigenvalue interlacing
• Some Inequalities for the Largest Eigenvalue of a Graph
• Quasi-random graphs

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