Controls
Euler counters
V
0
E
0
F
1
V−E+F
—
V − E + F = ?
Planarity edge bound
E ≤ 3V − 6 : add edges to test
bounded face (shaded)
outer (unbounded) face — still counted!
edge just added
crossing / non-planar edge
In Planar build mode each edge that closes a cycle splits one face into two, so F goes up and V−E+F stays at 2. In K5/K3,3 mode the build flags the edge that pushes E past the planarity bound — proof the graph cannot be drawn without a crossing.
Drawing
Press Step to add the first edge.