On the Alspach conjecture (Q2726708)
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scientific article; zbMATH DE number 1621384
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Alspach conjecture |
scientific article; zbMATH DE number 1621384 |
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21 February 2002
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packings
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cycles
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0.92500544
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0.91858727
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0.9160961
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On the Alspach conjecture (English)
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The Alspach conjecture for \(n\) odd and \(\sum m_i= n(n-1)/2\) is that \(K_n\) can be packed with cycles of lengths \(m_i\). For \(n\) even and \(\sum m_i= n(n-2)/2\), the conjecture is that \(K_n\) can be packed with cycles of lengths \(m_i\) and a \(1\)-factor. The author proves that if the \(m_i\) are bounded by a linear function of \(n\) and if \(n\) is sufficiently large, then the Aspach conjecture is valid.
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