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Generalizing a result of \\cite{BHZ} in two different ways, in this paper we prove $r_{odd} \\left(K_{n,n}, K_{2,t} \\right)=\\frac{n}{t} + o(n)$ for all $t\\geq 2$, and $r_{odd} \\left(\\mathcal{K}^{(k)}_{n,\\dots,n}, \\mathcal{K}_{1,\\dots,1,2,2} \\right) = \\frac{n}{2} + o(n)$ for all $k\\geq 2$. 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