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Let G be a connected simple graph with n vertices and m edges. Prove that G...

Let G be a connected simple graph with n vertices and m edges. Prove that G contains at least m−n+ 1 different subgraphs which are polygons (=circuits). Note: Different polygons can have edges in common. For instance, a square with a diagonal edge has three different polygons (the square and two different triangles) even though every pair of polygons have at least one edge in common.

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