A Spectral Turán Theorem

Authors:
Fan Chung
Affiliations:
Department of Mathematics, University of California, San Diego, CA 92093-0112, USA (e-mail: fan@ucsd.edu)
Venue:
Combinatorics, Probability and Computing
Year:
2005

Citing 2
Cited 1

Eigen values and expanders

Combinatorica
A generalization of Turán's theorem

Journal of Graph Theory

Turán's theorem for pseudo-random graphs

Journal of Combinatorial Theory Series A

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Abstract

If all nonzero eigenvalues of the (normalized) Laplacian of a graph $G$ are close to 1, then $G$ is $t$-Turán in the sense that any subgraph of $G$ containing no $K_{t+1}$ contains at most $(1-1/t + o(1) ) e(G)$ edges where $e(G)$ denotes the number of edges in G.