I'm reading Harris/Hirst/Mossinghoff's: *Combinatorics and Graph Theory*. Here:

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I don't understand: For all $2$-colorings, it must have a $K\_p$ **and** $K\_q$ or it must have a $K\_p$ **or** a $K\_q$? I'm confused: If it's the second option, a $K\_2$ does have a $K\_2$. But it's not clear that it actually speaks as if it were the first option.