Decomposition of \(K_{m,n}\) into short cycles (Q1292828)
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scientific article; zbMATH DE number 1322012
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Decomposition of \(K_{m,n}\) into short cycles |
scientific article; zbMATH DE number 1322012 |
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Decomposition of \(K_{m,n}\) into short cycles (English)
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10 April 2000
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It is shown that if \(m\), \(n\) are even integers, \(m\geq 4\), \(n\geq 6\), then the complete bipartite graph \(K_{m,n}\) can be decomposed into \(p\) copies of \(C_4\), \(q\) copies of \(C_6\) and \(r\) copies of \(C_8\) (where \(C_i\) is the cycle of length \(i\)) whenever \(4p+ 6q+ 8r= m\cdot n\). A similar result is obtained for \(K_{m,n}-F\) (\(F\) a 1-factor) when \(n\) is odd.
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decomposition
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complete bipartite graph
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cycle
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