For every fixed t and k, r_odd(K_{n,n}, K_{2,t}) = n/t + o(n) and r_odd(K^{(k)}_{n,...,n}, K_{1,...,1,2,2}) = n/2 + o(n).
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Odd Ramsey numbers of multipartite graphs and hypergraphs
For every fixed t and k, r_odd(K_{n,n}, K_{2,t}) = n/t + o(n) and r_odd(K^{(k)}_{n,...,n}, K_{1,...,1,2,2}) = n/2 + o(n).