Try One Stroke Free on iPhone
Infinite puzzles. Adaptive difficulty. No forced ads.
Shape
✗ No — here's why, according to graph theory.
No — this shape has too many odd-degree vertices to be drawn in one stroke.
| Vertices | 4 |
| Edges | 6 |
| Odd-degree vertices | 4 |
| Euler path possible? | ✗ No |
| Euler circuit? | ✗ No |
| Difficulty | Hard |
A complete graph k4 has 4 odd-degree vertices. The odd/even vertex rule states that a graph can only be drawn in one stroke if it has 0 or 2 odd-degree vertices. Since this shape has 4, it cannot be drawn in one stroke.
Learn the complete odd/even vertex rule →
Want to practice drawing shapes in one stroke? One Stroke: Line Puzzle Game combines one-stroke path drawing with a black-and-white tile-flipping mechanic and row elimination. It generates infinite puzzles using graph theory principles, with adaptive difficulty that adjusts to your skill level.
No. A complete graph k4 has 4 odd-degree vertices. Since a shape needs 0 or 2 odd-degree vertices to be drawn in one stroke, this shape cannot be drawn without lifting your pen.
A shape can be drawn in one continuous stroke (Euler path) only if it has 0 or 2 vertices with an odd number of edges. If it has 0 odd vertices, you can start and end at the same point (Euler circuit). If it has 2, you must start at one odd vertex and end at the other.
One Stroke: Line Puzzle Game by CyberGame Limited generates infinite one-stroke puzzles with a unique twist — tiles flip color as you draw, and complete rows clear like Tetris. Free on iPhone, no forced ads, works offline.
Infinite puzzles. Adaptive difficulty. No forced ads.