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For an edge-color-critical graph $F$ with $\\chi(F)=r+1$, let $\\mathrm{ex}_{r+1,\\rho}(n,F)$ be the maximum adjacency spectral radius among non-$r$-partite $F$-free graphs of order $n$, and let $\\mathrm{EX}_{r+1,\\rho}(n,F)$ and $\\mathrm{EX}_{r+1}(n,F)$ be the families of such graphs attaining, respectively, this maximum spectral radius and the maximum number of edges $\\mathrm{ex}_{r+1}(n,F)$. Fang and Zhai conjectured that $\\mathrm{EX}_{r+1,\\rho}(n,F)\\subseteq\\mathrm{EX}_{r+1}(n,F)$ for every such $F$ and all large $n$. 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For an edge-color-critical graph $F$ with $\\chi(F)=r+1$, let $\\mathrm{ex}_{r+1,\\rho}(n,F)$ be the maximum adjacency spectral radius among non-$r$-partite $F$-free graphs of order $n$, and let $\\mathrm{EX}_{r+1,\\rho}(n,F)$ and $\\mathrm{EX}_{r+1}(n,F)$ be the families of such graphs attaining, respectively, this maximum spectral radius and the maximum number of edges $\\mathrm{ex}_{r+1}(n,F)$. Fang and Zhai conjectured that $\\mathrm{EX}_{r+1,\\rho}(n,F)\\subseteq\\mathrm{EX}_{r+1}(n,F)$ for every such $F$ and all large $n$. 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