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As a common generalization of Tur\\'an's theorem and Erd\\H{o}s-Gallai theorem on the Tur\\'an number of matchings, Alon and Frankl determined ${\\rm ex}(n,{\\cal H})$ for ${\\cal H}=\\{K_r,M_k\\}$, where $M_k$ is a matching of size $k$. Replacing $M_k$ by $P_k$, Katona and Xiao obtained the Tur\\'an number of ${\\cal H}=\\{K_r,P_k\\}$ for $r \\leq \\lfloor k/2 \\rfloor$ and sufficiently large $n$. 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The Tur\\'an number ${\\rm ex}(n,{\\cal H})$ is the maximum possible number of edges in an $n$-vertex graph which does not contain any member of $\\cal H$ as a subgraph. As a common generalization of Tur\\'an's theorem and Erd\\H{o}s-Gallai theorem on the Tur\\'an number of matchings, Alon and Frankl determined ${\\rm ex}(n,{\\cal H})$ for ${\\cal H}=\\{K_r,M_k\\}$, where $M_k$ is a matching of size $k$. Replacing $M_k$ by $P_k$, Katona and Xiao obtained the Tur\\'an number of ${\\cal H}=\\{K_r,P_k\\}$ for $r \\leq \\lfloor k/2 \\rfloor$ and sufficiently large $n$. 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