A simple graph is an ordered pair of sets $\,\Gamma:=(V\,E)\,$ such that
$\,E\subseteq\binom V2.\ $ Kuratowski graph of the first kind is
$\,K_n:=\left(V\,\,\binom V2\right),\,$ where $\,n:=|V|.\,$ And of the second type is

$$ K_{m\,n}\,:=\,(W\!\cup\!V\,\, \mu(W\times V)) $$

where $\,W\cap V=\emptyset,\,$ and

$$\,\mu(W\times V)\,:=\,\{\{w\,v\}:\, (w\,v)\in W\times V\} $$

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**Q1 (single)**  What is the least natural number $\,s\,$ such that every
edge red-green coloring of $\,K_s\,$ induces a red subgraph isomorphic to
$\,K_5\,$ or green subgraph isomorphic to $\,K_{3\,3}\,$ ? Call this number
$\,\mbox{RK}_{rg}.$

**Q2 (double)**  What is the least natural number $\,d\,$ such that every
edge red-green coloring of $\,K_d\,$ induces a unicolored subgraph (totally red or totally gree) isomorphic to $\,K_5\,$ or to $\,K_{3\,3}\,$ ? Call this number
$\,\mbox{RK}_{xx}.$

**Q3 (triple)**  What is the least natural number $\,D\,$ such that every
edge red-green coloring of $\,K_d\,$ induces two unicolored subgraphs of the same color, one isomorphic to $\,K_5\,$ and the other one to $\,K_{3\,3}\,$ ? Call
this number $\,\mbox{RK}_{YY}.$

>***REMARK**   Of course, the above questions allude to Kuratowski's characterization of planar graphs (the theorem covered even more than graphs).*