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Asymmetric Homomorphism Thresholds for Graphs of Large Odd Girth
We determine the asymmetric homomorphism threshold from graphs of odd girth at least $7$ to triangle-free graphs, showing that $δ_{\mathrm{hom}}(\{C_3,C_5\},\{C_3\})=\frac{1}{9}$. Equivalently, for every $\varepsilon>0$, every $n$-vertex graph of odd girth at least $7$ and minimum degree at least $(
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