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Three-Color Ramsey Numbers For Paths

Authors:

András?Gyárfás Miklós?Ruszinkó Gábor?N.?Sárk?zy? Endre?Szemerédi

Affiliation:

1.Computer and Automation Research Institute,Hungarian Academy of Sciences,Budapest,Hungary;2.Computer and Automation Research Institute,Hungarian Academy of Sciences,Budapest,Hungary;3.Computer Science Department,Worcester Polytechnic Institute,Worcester, MA,USA;4.Computer and Automation Research Institute,Hungarian Academy of Sciences,Budapest,Hungary;5.Computer Science Department,Rutgers University,New Brusnwick, NJ,USA

Abstract:

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. * 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.

Keywords:

KeywordHeading" >Mathematics Subject Classification (2000): 05C55 05C38

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