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  "body": "\n## Statement\n\nLet $G$ be a finite [[connected|0FFAYNMAJZ]] [[planar graph|029JQEK15B]], drawn in the plane with no crossing edges.\nLet $v$, $e$ and $f$ be the numbers of vertices, edges and faces of the drawing, where the unbounded face counts.\nThen $v - e + f = 2$.\n\n## Remarks\n\nProof idea: if the graph has a cycle, delete an edge of the cycle. This removes one edge and one face.\nAt the end you have a [[spanning tree|0FQ5B8S1ZC]], with $e = v - 1$ and $f = 1$.\nThe same formula holds for the vertices, edges and faces of a convex polyhedron.\n\n## Explanations\n\n### L1 human\n\nDraw a connected graph without crossings and count its vertices, edges and regions.\nVertices minus edges plus regions is always $2$. For a square, this is $4 - 4 + 2$.\n",
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  "name": "Euler's formula for planar graphs",
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