The genus 2 crossing number of \(K_ 9\) (Q1901042)
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scientific article; zbMATH DE number 810266
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The genus 2 crossing number of \(K_ 9\) |
scientific article; zbMATH DE number 810266 |
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The genus 2 crossing number of \(K_ 9\) (English)
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29 October 1995
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A conjecture of \textit{P. C. Kainen} [J. Comb. Theory, Ser. B 12, 287-298 (1972; Zbl 0237.05104)] implies that the genus 2 crossing number of \(K_9\) is 3. In the present paper, the author disproves the conjecture, by showing that the actual value is \(\text{cr}_2(K_9)= 4\). The method involves demonstrating that certain genus 2 imbeddings of \(K_8\) are not possible.
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genus
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crossing number
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imbeddings
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