  For all positive integers $r\geq 3$ and $n$ such that $r^2-r$ divides $n$ and
an affine plane of order $r$ exists, we construct an $r$-edge colored graph
with minimum degree $(1-\frac{r-2}{r^2-r})n-2$ such that the largest
monochromatic component has order less than $\frac{n}{r-1}$. This generalizes
an example of Guggiari and Scott and, independently, Rahimi for $r=3$ and thus
disproves a conjecture of Gy\'arf\'as and S\'ark\"ozy for all integers $r\geq
3$ such that an affine plane of order $r$ exists.
