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
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The inequality λ₁(G)^r ≤ ∑ w_r(v) ⋅ (c_G(v)−1)/c_G(v) holds for every finite simple graph G and r ≥ 1, confirming the Kannan-Kumar-Pragada conjecture.
citing papers explorer
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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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A local Tur\'an inequality for walks and the spectral radius
The inequality λ₁(G)^r ≤ ∑ w_r(v) ⋅ (c_G(v)−1)/c_G(v) holds for every finite simple graph G and r ≥ 1, confirming the Kannan-Kumar-Pragada conjecture.