Abstract
We show that in every r-coloring of the edges of K n 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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András Gyárfás: Research supported in part by OTKA Grant No. K68322.
Gábor N. Sárközy: Research supported in part by the National Science Foundation under Grant No. DMS-0456401 and by OTKA Grant No. K68322.
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Gyárfás, A., Sárközy, G.N. Size of Monochromatic Double Stars in Edge Colorings. Graphs and Combinatorics 24, 531–536 (2008). https://doi.org/10.1007/s00373-008-0811-y
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DOI: https://doi.org/10.1007/s00373-008-0811-y