Size of Monochromatic Double Stars in Edge Colorings

@article{Gyrfs2008SizeOM,
  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},
  year={2008},
  volume={24},
  pages={531-536}
}
We show that in every r -coloring of the edges of Kn there is a monochromatic double star with at least n(r+1)+r−1 r2 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 n(r+1)+r−1 r2+1 . 

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