# Ramsey graph for C4 graph

Does there exist a ramsey graph of C4 such that an induced subgraph has a monochromatic C4, no matter how the edges are colored?

• You need to write your question more carefully, with all the conditions. Mar 12 '20 at 1:05

If $$m\gt n$$ and $$p\gt n\binom m2$$ then the complete bipartite graph $$K_{m,p}$$ has the property that, in any edge coloring with at most $$n$$ colors, it has a monochromatic induced subgraph $$K_{2,2}=C_4$$.
I.e., if $$n$$ is finite, we can take $$m=n+1$$ and $$p=n\binom{n+1}2+1$$, while if $$n=\aleph_\alpha$$ we can take $$m=\aleph_{\alpha+1}$$ and $$p=\aleph_{\alpha+2}$$.