The Ramsey numbers of large cycles versus small wheels

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Surahmat and Baskoro, E.T. and Broersma, H.J. (2002) The Ramsey numbers of large cycles versus small wheels. [Report]

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Abstract:
For two given graphs $G$ and $H$, the \textit{Ramsey number} $R(G,H)$ is the smallest positive integer $N$ such that for every graph $F$ of order $N$ the following holds: either $F$ contains $G$ as a subgraph or the complement of $F$ contains $H$ as a subgraph. In this paper, we determine the Ramsey number $R(C_n,W_{m})$ for $m=4$ and $m=5$. We show that $R(C_{n},W_{4})=2n-1$ and $R(C_n,W_5)=3n-2$ for $n\geq 5$. For larger wheels it remains an open problem to determine $R(C_n,W_{m})$.
Item Type:Report
Additional information:Imported from MEMORANDA
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Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/65821
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