The Ramsey number \(R(C_8,K_8)\) (Q1011781)
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scientific article; zbMATH DE number 5542428
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Ramsey number \(R(C_8,K_8)\) |
scientific article; zbMATH DE number 5542428 |
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The Ramsey number \(R(C_8,K_8)\) (English)
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9 April 2009
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It was conjectured by \textit{P. Erdős}, \textit{R.J. Faudree}, \textit{C.C Rousseau} and \textit{R.H. Schelp} in [J. Graph Theory 2, 53--64 (1978; Zbl 0383.05027)] that the Ramsey number \(R(C_m, K_n) = (m - 1)(n - 1) + 1\) for \(m \geq n\) except for \((m, n) = (3, 3)\). The Conjecture has been verified for \(m \leq 7\). It is shown that \(R(C_8, K_8) = 50\), which is a start on the verification of the Conjecture for \(m = 8\).
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Ramsey number
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cycles
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complete graph
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0.9304374
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0.9080827
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0.8852218
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