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It is known that the $r$-colored Ramsey number for $P$ is $R(P;r)=r+6$ for $r=2,3$, and that $R(P;r)\\le 3r$ for all $r\\ge3$. The latter result follows by a standard application of the Tur\\'an number $ex_3(n;P)$, which was determined to be $\\binom{n-1}2$ in our previous work. We have also shown that the full star is the only extremal 3-graph for $P$. In this paper, we perform a subtle analysis of the Tur\\'an numbers for $P$ under some additional restrictions. 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