arXiv:2611.03878v1 Announce Type: new Abstract: In this paper we study a relatively new Ramsey type graph parameter introduced by my Bachelor's thesis supervisor N\'ora Alm\'asi, and her Master's thesis supervisor Maria Axenovich. The parameter $\xi(G)$ denotes the largest natural number $n$, such that there is a red-blue-green edge coloring of $K_n$, such that in the edge coloring all copies of $G$ represent all three colors. After a brief recap on Ramsey numbers, we precisely define $\xi(G)$, and take a look at its relations to the Ramsey numbers. In the third chapter we establish lower bounds on $\xi(G)$, in the cases $G=K_5$ and $G=K_6$, namely $\xi(K_5)\ge 19$ and $\xi(K_6)\ge 31$.
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