Let G be an Eulerian graph. Prove that it is possible to partition the edge set of G

Chapter 51, Problem 51.6

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Let G be an Eulerian graph. Prove that it is possible to partition the edge set of G such that the edges in each part of the partition form a cycle of G. The figure shows such a partition in which the edges from different parts of the partition are drawn in different colors and line styles.

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