Need help understanding graph theory question Suppose that $l$ lines are drawn through a circle and these lines form $p$ points of
intersection (involving exactly two lines at each intersection). How many regions
$r$ are formed inside the circle by these lines? Assume that the lines end at the
edge of the circle at $2l$ distinct points.
The answer in the book is $r-1=e-v+1=p+l+1$
But I believe that the correct answer is $p-l+1$
I was told that $v = p+2l$ and $e =\frac{1}{2} \text{(sum of degrees)} = 2p+3l$
But im not sure how that all connects to $r-1=e-v+1=p+l+1$
Im $99\%$ sure that this is a typo and that it's supposed to be $r-1=e-v+1=p-l+1$
Am I Wrong?
$$r-1=e-v+1=(2p+3l)-(p+2l)+1=p+l+1$$
You can tell $p-l+1$ is wrong if you draw multiple lines without intersection.
Number of regions cannot be $\le 0$.
$$r-1=e-v+1=(2p+3l)-(p+2l)+1=p+l+1$$
You can tell $p-l+1$ is wrong if you draw multiple lines without intersection.
Number of regions cannot be $\le 0$.