Question: Suppose that G is a connected multigraph with 2k vertices of odd degree. Show that there exist k subgraphs that have G as their union,

Suppose that G is a connected multigraph with 2k vertices of odd degree. Show that there exist k subgraphs that have G as their union, where each of these subgraphs has an Euler path and where no two of these subgraphs have an edge in common.

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