Bounded VC-Dimension Implies the Schur-Erd?s Conjecture

In 1916, Schur introduced the Ramsey number r(3; m), which is minimum integer n > 1 such that for any m-coloring of edges complete graph Kn, there a monochromatic copy K3. He showed m) ? O(m!), and simple construction demonstrates ? 2?(m). An old conjecture Erd?s states = 2?(m). this note, we prove m-colorings with bounded VC-dimension, is, property set system induced by neighborhoods vertices respect to each color class has VC-dimension.