Planar Graphs Practice Problems Online

Is this graph planar?

Suppose a graph $G$ is not planar. If we add an edge to $G$ to connect two previously disconnected nodes to create the graph $G'$ , is $G'$ planar?

Suppose that there are three houses $A, B, C$ and three utilities 1, 2, and 3 each of which needs to be connected by a wire to all three houses. Assuming the utilities and the houses are all points (nodes), is there a way to position them and the wires (edges) such that no two wires overlap?

Note: this is the same as asking whether $K_{3,3}$ is a planar graph.

Suppose $G$ is a planar graph. If we create $G'$ by adding a single edge to $G$ , is $G'$ planar?

Concept Quizzes

Challenge Quizzes

Planar Graphs

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.