10217

# Is This Graph Planar?

A graph is planar if it can be drawn in the plane in such a way that no two edges meet except at a vertex with which they are both incident. Any such drawing is a plane drawing of . A graph is nonplanar if no plane drawing of exists. Trees, path graphs, and graphs having less than five vertices are planar. Although since as early as 1930 a criterion for a graph to be planar was known (Kuratowski's theorem), it turned out to be difficult to use. In this Demonstration we have chosen a selection of graphs for you to test for planarity. They form a small selection of the many available in Mathematica 8. By dragging the vertices, either conjecture that it is nonplanar or try to unravel a chosen graph to get a planar drawing (if a graph is planar, this procedure will be successful, as any planar graph has a drawing in which every edge is represented by a straight line). The purpose of this Demonstration is to give you an intuitive feeling for the complexity behind a method to automatically test for planarity.

### PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.