R(K_{2,n}, C_m) equals m+1 for m at least 3n+4, proving C_m is K_{2,n}-good in this range, with a disproof for even m when n is at least m+2.
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On Ramsey goodness of $K_{2,n}$ versus cycles
R(K_{2,n}, C_m) equals m+1 for m at least 3n+4, proving C_m is K_{2,n}-good in this range, with a disproof for even m when n is at least m+2.