Que subgraph of G and every edge of G appears in exactly one subgraph H₂. Complete the proof below of the following statement by using induction on the number of edges: Recall that a graph G decomposes into graphs H₁, H₂, ..., Ht if each H₂ is a Every even graph decomposes into cycles. Proof. We use induction on the number of edges in G, which we denote by m. Basis step: m = Induction step: Let G be an even graph with m edges, where m≥ 1, and assume that any even graph with fewer than m edges can be decomposed into cycles.

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