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Stability of the path–path Ramsey number

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

Book ID
108114132
Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
404 KB
Volume
309
Category
Article
ISSN
0012-365X

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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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For bipartite graphs G1,G2 ..... Gk, the bipartite Ramsey number b(GI,G2,...,Gk) is the least positive integer b so that any colouring of the edges of Kb, b with k colours will result in a copy of Gi in the ith colour for some i. In this note, we establish the exact value of the bipartite Ramsey num