Scott asked the question of determining c d such that if D is a digraph with m arcs and minimum outdegree ? 2 then V ( ) has partition 1 , min { e } m, where (respectively, number from to ). Lee, Loh, Sudakov showed = ? 6 + o 3 5 conjectured ? for 4. In this paper, we show 4 14 prove some partial results 5.

We show that if a coloring of the plane has properties any two points at distance one are colored differently and is partitioned into uniformly triangles under certain conditions, then it requires least seven colors. This also true for using polygons point bordering four polygons.