Planar graph

Definition

A graph $G$ is planar if it has a drawing in the plane in which no two edges cross. In such a drawing, the vertices are distinct points of $\mathbb{R}^2$, and each edge $uv$ is a simple arc from $u$ to $v$. Two arcs meet only at a common end, and an arc contains no vertex other than its ends.

Remarks

A drawing of this kind is a plane graph, or an embedding of $G$ in the plane. The complete graph $K_4$ is planar. $K_5$ and $K_{3,3}$ are not planar. Kuratowski's theorem characterizes the finite planar graphs by these two graphs.

Explanations

L1 human

A graph is planar when you can draw it on paper with no crossing edges. A map of countries gives a planar graph: one vertex for each country, and an edge between neighbours.