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On Ramsey numbers for paths versus wheels

โœ Scribed by A.N.M. Salman; H.J. Broersma

Book ID
108113604
Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
401 KB
Volume
307
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 twoโ€coloring of the edges of the complete tripartite graph __K__(__n__, __n__, __n__) there is a monochromatic path of length (1 โˆ’ __o__(1))2__n__. Since __R__(__P__~2__n__+1~,__P__~2__n__+1~)=3__n__,

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For two given graphs G 1 and G 2 , the Ramsey number R(G 1 , G 2 ) is the smallest integer n such that for any graph G of order n, either G contains G 1 or the complement of G contains G 2 . Let C n denote a cycle of order n and W m a wheel of order m + 1. It is conjectured by Surahmat, E.T. Baskoro