A 4-color theorem of the Klein bottle (Q1825877)
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scientific article; zbMATH DE number 4122016
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A 4-color theorem of the Klein bottle |
scientific article; zbMATH DE number 4122016 |
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A 4-color theorem of the Klein bottle (English)
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1989
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It is well known that the chromatic number of a graph embeddable in the Klein bottle does not exceed 6. The author proves that if the girth g of such a graph satisfies \(4\leq g\leq 5\) or \(g\geq 6\) then the upper bound on the chromatic number is 4 or 3, respectively. These bounds are sharp for all g except, possibly, \(g=5.\)
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graph embeddings
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Klein bottle
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chromatic number
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