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Math Help - Euler and Hamilton circuits

  1. #1
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    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.

    Thank you in advance
    Attached Thumbnails Attached Thumbnails Euler and Hamilton circuits-euler.jpg   Euler and Hamilton circuits-hamilton.jpg   Euler and Hamilton circuits-hamilton2.jpg  
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  2. #2
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    Can you state the definitions needed to solve thes two problems?
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  3. #3
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    no, do you?
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  4. #4
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    Quote Originally Posted by Narek View Post
    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
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  5. #5
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    Quote Originally Posted by Plato View Post
    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
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  6. #6
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    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.
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