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

  • 4
    $\begingroup$ You need to write your question more carefully, with all the conditions. $\endgroup$ Mar 12, 2020 at 1:05

1 Answer 1


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 $p=\aleph_{\alpha+2}$.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.