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Tripartite Ramsey numbers for paths

✍ Scribed by András Gyárfás; Miklós Ruszinkó; Gábor N. Sárközy; Endre Szemerédi

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
137 KB
Volume
55
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

In this article, we study the tripartite Ramsey numbers of paths. We show that in any two‐coloring of the edges of the complete tripartite graph K(n, n, n) there is a monochromatic path of length (1 − o(1))2__n__. Since R(P~2__n__+1~,P~2__n__+1~)=3__n__, this means that the length of the longest monochromatic path is about the same when two‐colorings of K~3__n__~ and K(n, n, n) are considered. © 2007 Wiley Periodicals, Inc. J Graph Theory 55: 164–174, 2007

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