#graphs **Theorem.** There is a graph with no uncountable clique and no uncountable anticlique. **Proof.** Define a graph on $\mathbb{R}$ - let $\leq$ be the regular order and $\trianglelefteq$ a well order. Define $xEy$ iff $\leq$ and $\trianglelefteq$ agree on $x,y$. Let $A\subseteq \mathbb{R}$ be uncountable. Consider the increasing enumeration of $A$ under $\trianglelefteq$. If it is a clique, i.e. $\forall x,y\in A$ $\leq$ and $\trianglelefteq$ agree on $x,y$, then we get an uncountable increasing in $\leq$ sequence, and if it's an anticlique we get an uncountable decreasing sequence in $\leq$, both of which are impossible. **Remark.** As a consequence, it is neither countably chromatic nor uncountably chromatic. **Remark.** We can also take any uncountable subgraph and it'll have the same properties.