For color-critical F with χ(F)=r+1≥4, λ²(G) ≥ 2(1-1/r)m + q implies N_F(G) ≥ (B_F - o(1)) q m^{(f-2)/2} for small q, with sharp B_F = α_F/4 ⋅ (2r/(r-1))^{f/2}.
Nikiforov, On a theorem of Nosal, (2021), arXiv:2104.12171
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Sidorenko's conjecture is equivalent to hom(H,G) ≥ λ(G)^{2e-v} M(G)^{v-e}, which yields asymptotically sharp supersaturation bounds for the number of K_{t,t} and C_{2t} in graphs with λ(G) > λ(S_{t-1,m}).
The paper establishes asymptotic lower bounds on shared-edge triangles, shared-vertex cliques, and C4 copies in graphs with spectral radius > √m, confirming three conjectures with matching constructions.
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An edge-spectral supersaturation of Mubayi's theorem for color-critical graphs
For color-critical F with χ(F)=r+1≥4, λ²(G) ≥ 2(1-1/r)m + q implies N_F(G) ≥ (B_F - o(1)) q m^{(f-2)/2} for small q, with sharp B_F = α_F/4 ⋅ (2r/(r-1))^{f/2}.
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Spectral Sidorenko inequalities and edge-spectral supersaturation
Sidorenko's conjecture is equivalent to hom(H,G) ≥ λ(G)^{2e-v} M(G)^{v-e}, which yields asymptotically sharp supersaturation bounds for the number of K_{t,t} and C_{2t} in graphs with λ(G) > λ(S_{t-1,m}).
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More on Nosal's spectral theorem: Books and $4$-cycles
The paper establishes asymptotic lower bounds on shared-edge triangles, shared-vertex cliques, and C4 copies in graphs with spectral radius > √m, confirming three conjectures with matching constructions.