# Thread: Euler and Hamilton circuits

1. ## 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.

2. Can you state the definitions needed to solve thes two problems?

3. no, do you?

4. 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

5. 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

6. ## 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
but if there is a circuit, I don't know how to construct the circuit.