Euler's Solution
 
 
 
 
 
 
Euler's graph for the Koingsberg Bridge Problem
 
 
To analyize this graph lets look at the degree of the verticers and if they are even or odd.
 
 
 
 
 
 

 
 
Vertex
Degree of Vertex
Even / Odd
A
5
odd
B
3
odd
C
3
odd
D
3
odd
 
 
 

From this we can apply theorm 2 from Euler's theorems.  Since we have more than two odd nodes the graph is not traversable.  Euler concluded that the people of Kaliningrad were not able to walk across all the bridges only once.

What could we add to this graph in order to make it traversable?

Give it a try then check out what the town of Kaliningrad did.
 
 

 

   Koingsberg Bridge Problem            Go back to look at Euler's process
 
 
 
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