The possible number of cycles in cycle systems (Q2760988)
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scientific article; zbMATH DE number 1682802
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The possible number of cycles in cycle systems |
scientific article; zbMATH DE number 1682802 |
Statements
17 December 2001
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cycles
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edge decomposition
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0.84795344
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0.83594185
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The possible number of cycles in cycle systems (English)
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A theorem of graph theory is proved. Let \(G_n\) be the complete graph \(K_n\) for odd \(n\) and \(K_n\) minus the perfect matching for even \(n\), and let \(e_n\) be the number of edges of \(G_n\). The edge set \(E(G_n)\) can be partitioned into \(t\) cycles if and only if \(t\) lies in the interval \([e_n/n,e_n/3]\).
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