The Ramsey number (Q540088)
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scientific article; zbMATH DE number 5903020
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Ramsey number |
scientific article; zbMATH DE number 5903020 |
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The Ramsey number (English)
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1 June 2011
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Summary: 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 \(K_m\) denote a complete graph of order \(m\) and \(K_n - P_3\) a complete graph of order \(n\) without two incident edges. In this paper, we prove that \(r(K_5 - P_3, K_5) = 25\) without help of computer algorithms.
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