Graph theory

Planarity Untangler

To advance to the next level, drag the vertices (dots) until the crossing edges (lines) disappear. Graphs that can be rearranged to have no crossing edges are 'planar'; graphs that cannot are non-planar. If you think a graph is non-planar, hit the yellow button on the left. But be careful - if you're wrong, you'll go back to Level 1!

Current problem

Level 1

Untangle the graph, or decide that it cannot be drawn without crossings.

Editing mode

Actions

Display

Show degrees Show vertex labels Highlight crossings

Graph info

Vertices: 0
Edges: 0
Crossings: 0

Keyboard

V vertex mode, E edge mode, D degrees, Delete remove selected, Ctrl+Z/Ctrl+Y undo/redo.

Untangle challenge

Crossings in the starting picture do not always mean the graph is impossible. Try moving the vertices first.