Cycle decompositions of the line graph of \(K_ n\) (Q1208048)
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scientific article; zbMATH DE number 165757
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Cycle decompositions of the line graph of \(K_ n\) |
scientific article; zbMATH DE number 165757 |
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Cycle decompositions of the line graph of \(K_ n\) (English)
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16 May 1993
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A 4-cycle system of a graph \(G\) is a set of 4-cycles that induces a partition of the edge set of \(G\). This note supplements a result of K. Heinrich and G. M. Nonay about a certain set of 4-cycles of \(K_ n\). The proof of the result used a 4-cycle system of the line graph of \(K_ n\). Here the following theorem is proved: If \(n\equiv 1\pmod 8\), then there exists a 4-cycle system of the line graph of \(K_ n\).
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cycle decomposition
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line graph
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