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# Graph theory help? watch

1. I need to figure out given a degree sequence whether or not there exists a graph, if it does then draw it if it doesn't explain why it doesn't.

I'm asked here if (0,1,2,2,3) exists without a triangle and I'm not too sure how to move forward I can't seem to draw one but I can't figure out how to explain that one doesn't exists either.

Any help on this one and other questions like it?

Cheers.
2. (Original post by poorform)
I need to figure out given a degree sequence whether or not there exists a graph, if it does then draw it if it doesn't explain why it doesn't.

I'm asked here if (0,1,2,2,3) exists without a triangle and I'm not too sure how to move forward I can't seem to draw one but I can't figure out how to explain that one doesn't exists either.

Any help on this one and other questions like it?

Cheers.
Take the vertices one at a time.

Let the first vertex have degree 0

Let the second vertex have degree 1. It is connected to just one other vertex. That vertex has either degree 2, or 3,...

It helps to construct a diagram as you go.

And for clarity of expression you may like to label the vertices a0, a1, etc.
3. (Original post by ghostwalker)
Take the vertices one at a time.

Let the first vertex have degree 0

Let the second vertex have degree 1. It is connected to just one other vertex. That vertex has either degree 2, or 3,...

It helps to construct a diagram as you go.

And for clarity of expression you may like to label the vertices a0, a1, etc.
I tried that and kept ending up not being able to construct the graph,
4. (Original post by poorform)
I tried that and kept ending up not being able to construct the graph,
Presumably you've done it rigorously, then you've shown that no such graph exists.

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