Triangle-free graphs with large chromatic numbers (Q1969797)
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scientific article; zbMATH DE number 1417412
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Triangle-free graphs with large chromatic numbers |
scientific article; zbMATH DE number 1417412 |
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Triangle-free graphs with large chromatic numbers (English)
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15 September 2000
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It is shown that there are two positive constants \(c_1, c_2\) such that the maximum possible chromatic number of a triangle-free graph with \(m>1\) edges is at most \(c_1m^{1/3}/(\log m)^{2/3}\) and at least \(c_2m^{1/3}/(\log m)^{2/3}\). This settles a problem of Erdős.
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triangle-free graphs
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chromatic number
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