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Many years ago, Erd\\H{o}s, Faudree, Schelp and Simonovits proposed the study of the function $\\phi(n,d,k)$, and conjectured that for any positive integers $n>d\\geq k$, it holds that $\\phi(n,d,k)\\leq \\lfloor\\frac{k-1}{2}\\rfloor\\lfloor\\frac{n}{d+1}\\rfloor+\\epsilon$, where $\\epsilon=1$ if $k$ is odd and $\\epsilon=2$ otherwise. 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