# Euler and Hamilton circuits

• Nov 5th 2008, 11:55 AM
Narek
Euler and Hamilton circuits
1) for the first picture:
determine whether each graph has an Euler circuit. Construct such a circuit when one exists.

2) for the rest 2 pictures
determine whether the given graph has a Hamilton circuit. if it does, find such a circuit. if it doesnt, give an argument to show why not such circuit exists.

• Nov 5th 2008, 12:27 PM
Plato
Can you state the definitions needed to solve thes two problems?
• Nov 5th 2008, 12:37 PM
Narek
no, do you?
• Nov 5th 2008, 03:55 PM
Plato
Quote:

Originally Posted by Narek
no, do you?

Well I certainly hope so, I do teach this.
Mathematics is definitional driven,
Those who do not know the definitions cannot do mathematics
• Nov 5th 2008, 11:47 PM
Narek
Quote:

Originally Posted by Plato
Well I certainly hope so, I do teach this.
Mathematics is definitional driven,
Those who do not know the definitions cannot do mathematics

yes i believe you! I do NOT know it, and thats why I am asking it here. if you teach, then you can teach here. If I knew the answers and definitions, I wouldn't be here asking (Happy)
• Nov 5th 2008, 11:58 PM
Narek
MY DEFINITION
the condition for a graph to have Euler circuit is the degrees of all vertices should be even, so in the first picture we have two vertices (b ; c) that they have odd degree.
So I think for the first picture, it doesn't have Euler circuit but with consideration of existence of two vertices of odd degree, we can say this graph have Euler path (Rofl)
but if there is a circuit, I don't know how to construct the circuit.