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February 13th, 2013, 10:10 PM   #11
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Re: drawing a closed figure

Quote:
Originally Posted by mathmaniac
Then can you post it?
I thought I had one proof, but now I think it has some flaws in it. Although, I am not an expert in graph theory. But I can assure you that soroban's conditions are not true. There are graphs which are not Eulerian, not even Hamiltonian, even though it's traceable.
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February 14th, 2013, 07:03 PM   #12
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Re: drawing a closed figure

Balarka,I see nothing wrong with soroban's conjecture.I draw a lot of figures and everything was fine.I am trying to work out a proof.
Let us ask him how did he reach the conjecture.
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February 14th, 2013, 07:45 PM   #13
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Re: drawing a closed figure

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I see nothing wrong with soroban's conjecture
GP(5, 2) is the first counterexample. This figure has ten odd nodes and no even nodes, even though it is traceable. soroban gave the properties of an Eulerian graph, but there are traceable ones which are not Hamiltonian. I doubt there is a general criteria for traceability.
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February 14th, 2013, 07:50 PM   #14
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Re: drawing a closed figure

Can you post the pic?
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February 14th, 2013, 08:33 PM   #15
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Re: drawing a closed figure

Sure. Well, you can search it in the net--its the peterson graph :

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May 13th, 2013, 07:36 PM   #16
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Re: drawing a closed figure

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Originally Posted by mathbalarka
I thought I had one proof, but now I think it has some flaws in it.
For a graph that is traceable from all vertices other than the first and last goes two lines,one reaching it and one out of it.There could be no line reaching the 1st one if the first and last and are not the same and there could also be no line going out of the last one.That makes the maximum odd vertices 2.

Quote:
the peterson graph
Can you show how to trace it in one go without repeating a path?
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May 6th, 2015, 10:30 PM   #17
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It's interesting Post to question and answer
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