A note about monochromatic components in graphs of large minimum degree

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