Cycle decompositions of the line graph of \(K_ n\). (English) Zbl 0777.05076
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 \(K_ n\).
Reviewer: N.F.Quimpo (Manila)
MSC:
| 05C38 | Paths and cycles |
| 05C70 | Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) |
References:
| [1] | Heinrich, K.; Nonay, G., Exact coverings of 2-paths by 4-cycles, J. Combin. Theory Ser. A, 45, 50-61 (1987) · Zbl 0675.05044 |
| [2] | Sotteau, D., Decomposition of \(Km,n(K∗m,n)\) into cycles (circuits) of length 2k, J. Combin. Theory Ser. B, 30, 75-81 (1981) · Zbl 0463.05048 |
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