On a problem of Erdős and Rado (Q1387613)
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scientific article; zbMATH DE number 1160055
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a problem of Erdős and Rado |
scientific article; zbMATH DE number 1160055 |
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On a problem of Erdős and Rado (English)
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6 September 1998
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Improved upper and lower bounds for the digraph Ramsey numbers \(r(K_n^*,L_m)\) are verified, where \(r(K_n^*,L_m)\) is the smallest integer \(p\) such that any digraph of order \(p\) contains either an independent set with \(n\) vertices or a transitive tournament of order \(m\). For example, it is shown that \(r(K_n^*, L_3) \leq n^2\), and in particular that \(13 < r(K_4, L_3) \leq 16\). Recursive upper bounds are given that improve on previous bounds of Erdős and Rado, and also of Bermond.
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tournaments
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directed graphs
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Ramsey numbers
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