Size of Monochromatic Double Stars in Edge Colorings

  title={Size of Monochromatic Double Stars in Edge Colorings},
  author={Andr{\'a}s Gy{\'a}rf{\'a}s and G{\'a}bor N. S{\'a}rk{\"o}zy},
  journal={Graphs and Combinatorics},
We show that in every r-coloring of the edges of Kn there is a monochromatic double star with at least $$\frac{n(r+1)+r-1}{r^2}$$ vertices. This result is sharp in asymptotic for r = 2 and for r≥ 3 improves a bound of Mubayi for the largest monochromatic subgraph of diameter at most three. When r-colorings are replaced by local r-colorings, our bound is $$\frac{n(r+1)+r-1}{r^2+1}$$. 

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