The authors confirm Guiduli's spectral conjecture in strengthened form and prove that the spectral Turán threshold exactly detects the edge Turán threshold for all r and n, with equality cases.
Nosal, Eigenvalues of Graphs, Master Thesis, University of Calgary, 1970
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On spectral Tur\'an theorems: confirming a conjecture of Guiduli and two problems of Nikiforov
The authors confirm Guiduli's spectral conjecture in strengthened form and prove that the spectral Turán threshold exactly detects the edge Turán threshold for all r and n, with equality cases.