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.
Erd˝ os, Some recent progress on extremal problems in graph theory, in: Proceedings of the Sixth Southeastern Conference on Combinatorics, Graph Theory and Computing, pp
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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.