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case, let p be an edge in a cycle in G. Let G’ be the graph of G with edge P removed, i.e. G’=(V,E\{p}). This gives the relationship |E’| = |E|-1. Since p was an edge in a cycle, it separated 2 distinct faces, so removing it reduces the number of faces for G’. Namely |F’| = |F|-1. Since G has n+1