A Simple Graph Theory

1. GRAPH
THEORY

5. THE SEVEN BRIDGES OF
KÖNIGSBERG, GERMANY

6. Leonhard Euler
Konigsberg Bridge Problem

10. A
B
C
D
A
B
C
D

11. A
BC
D E

12. Degree 0 Degree 1 Degree 2 Degree 3 Degree 4

13. A graph will contain an Euler path if it contains at most two vertices of odd degree.
A
B C D
EF F
A B C
DE

14. A graph will contain an Euler circuit if all vertices have even degree.
A
B C D
EF A
B C D
E
F
G

15. Why do we care an Euler circuit exist. For example the police officer wanted to
patrol on a neighborhood on walking as little as possible. The ideal would be a
circuit that covers every street with no repeats. That's an Euler circuit! Luckily Euler
solved the question of whether or not an Euler path or circuit will exist.

16. Thanks