MHB How to show a graph contains no Hamilton cycles?

AI Thread Summary
The discussion centers on proving that a specific graph does not contain Hamilton cycles by demonstrating that all possible routes starting from vertex b close a cycle while leaving some vertices disconnected. The user seeks a more efficient method for this proof and inquires about general procedures for showing the absence of certain structures in graphs. Several algorithms relevant to this problem are mentioned, with a recommendation to read specific resources for further understanding. The conversation emphasizes the importance of exploring established methods in graph theory for such proofs. Overall, the exchange highlights the need for efficient strategies in graph analysis.
annie122
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Here is the graph in question:
a1642v.jpg


The edges in red are the paths that must be included in the cycle, since vertices
a, k, e, and o have only degree 2.
I listed all possible routes starting from vertex b, and showed that they all routes closes a cycle while leaving some vertex disconnected.

Is there a more efficient way?
In general, when asked to show that a graph doesn't contain something, what is the usual procedure for proving it?
 
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Yuuki said:
Here is the graph in question:
a1642v.jpg


The edges in red are the paths that must be included in the cycle, since vertices
a, k, e, and o have only degree 2.
I listed all possible routes starting from vertex b, and showed that they all routes closes a cycle while leaving some vertex disconnected.

Is there a more efficient way?
In general, when asked to show that a graph doesn't contain something, what is the usual procedure for proving it?

Hi Yuuki, :)

Several algorithms to solve this kind of a problem is discussed >>here<<. Specially you might like to read >>this<<.
 
Thank you for the reply for this thread and the other one.
I'll definitely read the PDF.
 
Yuuki said:
Thank you for the reply for this thread and the other one.
I'll definitely read the PDF.

You are welcome. (Handshake)
 

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