# 4-cycle Decompositions of the Cartesian Product of Two Complete Graphs

@inproceedings{PikeyDepartment20074cycleDO, title={4-cycle Decompositions of the Cartesian Product of Two Complete Graphs}, author={David A. PikeyDepartment}, year={2007} }

- Published 2007

In this paper we establish necessary and suucient conditions on m and n in order for KmKn, the cartesian product of two complete graphs, to be decomposable into cycles of length 4. The main result is that Km Kn can be decomposed into cycles of length 4 if and only if either m; n 0 (mod 2), m; n 1 (mod 8), or m; n 5 (mod 8).

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## Decomposition of Product Graphs into Paths and Cycles of Length Four

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