please help~graph theory problem 2

Quote:

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Originally Posted by MarkW

I've drawn a diagram of a subgraph that is a subdivision of K3,3:
http://img136.imageshack.us/img136/6504/k33fr0.png
The red vertices are the result of subdivisions, so they can be ignored. (there is also an edge from 7 to 8, but I forgot to draw it in)

What I want to know is, is this the answer to 2.a. or 2.b?

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do u mean that u forgot to draw the edge from 6 to 8??
and also, where is your vertex 0? 0 is an element of right?

can anyone give me a hint on how to solve question 2a?

Quote:

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Originally Posted by TomP

2a's got to do with Euler's Formula and the fact that:

2q = r*(no. edges in each region) > r*(length of shortest cycle)

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im a little confused i used Euler's formula and i got that the number of faces should be 9 which is clearly a lot less than it is in real life...is there any way i can work out the number of actual faces by looking at the graph? and also, where did u get the other formula from? and how do i calculate the number of edges in each region?