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.
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The paper proves the edge-local inequality λ^r(G) ≤ ∑_{uv∈E(G)} [(c_G(uv)−1)/c_G(uv)] (w_{r−1}(u) + w_{r−1}(v)) for r≥2, confirming the vertex-local conjecture and determining extremal graphs.
Extends localized Turán-type inequalities and spectral upper bounds on the largest eigenvalue to signed graphs, generalizing prior results for unsigned and signed graphs.
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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.
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Local Tur\'an inequalities for walks and the spectral radius
The paper proves the edge-local inequality λ^r(G) ≤ ∑_{uv∈E(G)} [(c_G(uv)−1)/c_G(uv)] (w_{r−1}(u) + w_{r−1}(v)) for r≥2, confirming the vertex-local conjecture and determining extremal graphs.
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Localization of spectral Tur\'an theorems for signed graphs
Extends localized Turán-type inequalities and spectral upper bounds on the largest eigenvalue to signed graphs, generalizing prior results for unsigned and signed graphs.