For sufficiently large n, an intersection-weighted sum over any k-uniform family is at most 1, with equality if and only if the family is a star.
Bradač,A generalization of Turán’s theorem
3 Pith papers cite this work. Polarity classification is still indexing.
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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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An Intersection-Weighted Erd\H{o}s-Ko-Rado Theorem
For sufficiently large n, an intersection-weighted sum over any k-uniform family is at most 1, with equality if and only if the family is a star.
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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.