The author shows that for every uncountable cardinal \(\lambda\) there exist \(2^\lambda\) graphs of size \(\lambda\) which are pairwise not comparable with respect to the minor relation. The construction involves results on stationary subsets of \(\lambda\). The existence of infinitely many uncountable minor-incomparable graphs was shown along different lines by R. Thomas [A counter-example to “Wagner’s conjecture” for infinite graphs, Math. Proc. Camb. Philos. Soc. 103, No. 1, 55-57 (1988; Zbl 0647.05054)].