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Three-color Ramsey numbers for paths

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

Publisher: Springer-Verlag
Year: 2008
Tongue: English
Weight: 325 KB
Volume: 28
Category: Article
ISSN: 0209-9683
DOI: 10.1007/s00493-008-2395-9

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Three-Color Ramsey Numbers For Paths

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## 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__,

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Exoo, G., Three color Ramsey number of K, -e, Discrete Mathematics 89 (1991) 301-305. We show that 28 s r(K4 -e; 3) G 32. The construction used to establish the lower bound is made by using the strongly regular Schllfli graph for one of the colors, and then by partitioning its complement into two i

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I Retaefltiy, Ramsey numbers have been obtained for several &sses of graphs. In particthey have been studied for hs of low wder, pairs of paths, paks of cycles, and for a . In this paper, th rs atie obtained fair aI3 pa&cycle pairs,