Coloring the square of a \(K_{4}\)-minor free graph (Q1402088)
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scientific article; zbMATH DE number 1967281
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Coloring the square of a \(K_{4}\)-minor free graph |
scientific article; zbMATH DE number 1967281 |
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Coloring the square of a \(K_{4}\)-minor free graph (English)
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19 August 2003
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Let \(G\) be a \(K_4\)-minor free graph with maximum vertex degree \(\Delta\). The authors show that the chromatic number of the square of \(G\) is at most \(\Delta+ 3\) if \(2\leq\Delta\leq 3\), and \(\lfloor 3\Delta/2\rceil+ 1\) if \(\Delta\geq 4\). The result is best possible.
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series-parallel graph
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\(K_4\)-minor free graph
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square
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chromatic number
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