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Three-Color Ramsey Numbers For Paths

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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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Authors and Affiliations

  1. Computer and Automation Research Institute, Hungarian Academy of Sciences, P.O. Box 63, Budapest, H-1518, Hungary

    András Gyárfás

  2. Computer and Automation Research Institute, Hungarian Academy of Sciences, P.O. Box 63, Budapest, H-1518, Hungary

    Miklós Ruszinkó*

  3. Computer Science Department, Worcester Polytechnic Institute, Worcester, MA, 01609, USA

    Gábor N. Sárközy†

  4. Computer and Automation Research Institute, Hungarian Academy of Sciences, P.O. Box 63, Budapest, H-1518, Hungary

    Gábor N. Sárközy†

  5. Computer Science Department, Rutgers University, New Brusnwick, NJ, 08903, USA

    Endre Szemerédi

Authors
  1. András Gyárfás
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  2. Miklós Ruszinkó*
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  3. Gábor N. Sárközy†
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  4. Endre Szemerédi
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Corresponding author

Correspondence to András Gyárfás.

Additional information

* 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.

An erratum to this article is available at http://dx.doi.org/10.1007/s00493-008-2395-9.

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Gyárfás, A., Ruszinkó*, M., Sárközy†, G.N. et al. Three-Color Ramsey Numbers For Paths. Combinatorica 27, 35–69 (2007). https://doi.org/10.1007/s00493-007-0043-4

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  • DOI: https://doi.org/10.1007/s00493-007-0043-4

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