I have an infinite graph $G$ and a natural number $n$, and I am interested in the property of $n$-colorability of $G$. I have the naive idea that
(1) if almost every partition of the vertices of $G$ into $n$ subsets is not an $n$-coloring, then $G$ is not $n$-colorable.
Of course, here I am being ambiguous as to what it means for something to hold for "almost every" partitions. Is there a notion of "almost every" for which (1) is true, or another for which (1) is false?