Three-Color Ramsey Numbers For Paths

An Erratum to this article was published on 01 July 2008

We prove—for sufficiently large n—the following conjecture of Faudree and Schelp:

$$ R{\left( {P_{n} ,P_{n} ,P_{n} } \right)} = \left\{ {\begin{array}{*{20}c} {{2n - 1{\kern 1pt} \;{\text{for}}\;{\text{odd}}\;n,}} \\ {{{\text{2n - 2}}\;{\text{for}}\;{\text{even}}\;n,}} \\ \end{array} } \right. $$

, for the three-color Ramsey numbers of paths on n vertices.

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Correspondence to András Gyárfás.

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* The second author was supported in part by OTKA Grants T038198 and T046234.

† Research supported in part by the National Science Foundation under Grant No. DMS-0456401.

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Gyárfás, A., Ruszinkó*, M., Sárközy†, G.N. et al. Three-Color Ramsey Numbers For Paths. Combinatorica 27, 35–69 (2007).

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Mathematics Subject Classification (2000):

  • 05C55
  • 05C38