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  "body": "\n## Definition\n\nA [[graph|0JD5C82QMB]] $G$ is planar if it has a drawing in the plane in which no two edges cross.\nIn such a drawing, the vertices are distinct points of $\\mathbb{R}^2$, and each edge $uv$ is a simple arc from $u$ to $v$.\nTwo arcs meet only at a common end, and an arc contains no vertex other than its ends.\n\n## Remarks\n\nA drawing of this kind is a plane graph, or an embedding of $G$ in the plane.\nThe complete graph $K_4$ is planar. [[$K_5$ and $K_{3,3}$ are not planar|030A3FHN14]].\n[[Kuratowski's theorem|0J6G5NJC5R]] characterizes the finite planar graphs by these two graphs.\n\n## Explanations\n\n### L1 human\n\nA graph is planar when you can draw it on paper with no crossing edges.\nA map of countries gives a planar graph: one vertex for each country, and an edge between neighbours.\n",
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