Graph theory puzzle

1. Shannon
Switching Game
GRAPH THEORY

2. What is a graph?

3. What is a graph?
GRAPH PLANAR GRAPH MULTIGRAPH PSEUDOGRAPH

4. The rules
 The game is played on a finite graph with two special vertices: A and B
 Each edge of the graph can be either coloured or removed
 The two players are called Short and Cut and they take turns to move
 On Cut’s turn they deletes a non-coloured edge of their choice (by crossing
it out)
 On Short’s turn they colour any edge that is still in the game (not crossed
out)
 Short is trying to get from point A to point B and Cut is trying to stop them
 If Cut manages to turn the graph into one where A and B are no longer
connected they win.
 If Short manages to create a coloured path from A to B they win.

5. Who will win?
A B
A B
A B
1)
2)
3)

6. Short aims at
building a path
between the two
yellow vertices. Cut
has to stop Short
from reaching this
goal.
space

7. Short aims at
building a path
between the two
white vertices. Cut
has to stop Short
from reaching this
goal.
space

8. Short aims at
building a path
between the two
white vertices. Cut
has to stop Short
from reaching this
goal.
space

9. Short aims at
building a path
between the two
green vertices. Cut
has to stop Short
from reaching this
goal.
space