Proves that λ3/n < 1/(2√2) - ε for some positive ε, i.e., Nikiforov's unproved strict bound for k=3, via a new graph operation and an analysis of the two smallest eigenvalues.
Improved lower bounds on the extrema of eigenvalues of graphs
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Strengthened upper bound on the third eigenvalue of graphs
Proves that λ3/n < 1/(2√2) - ε for some positive ε, i.e., Nikiforov's unproved strict bound for k=3, via a new graph operation and an analysis of the two smallest eigenvalues.